Therefore, the direction of force A (F) for the particle to be in equilibrium is 16 kN in the opposite direction of the sum of forces B and C.
How to determine the direction of force F for the particle to be in equilibrium?To determine the direction of force F for the particle to be in equilibrium, we need to consider the vector sum of forces acting on the particle. In equilibrium, the net force acting on the particle must be zero.
Force A (A) = 12 kN (unknown direction)
Force B (B) = 7 kN (unknown direction)
Force C (C) = 9 kN (known direction)
Let's denote the unknown direction of force A as θ.
To find the direction of force A, we'll use vector addition:
ΣF = A + B + C
Since the particle is in equilibrium, the net force ΣF must be zero:
ΣF = 0
Therefore, we can write the equation as:
0 = A + B + C
Substituting the magnitudes of the forces:
0 = 12 kN + 7 kN + 9 kN
0 = 28 kN
This equation implies that the sum of the magnitudes of forces A, B, and C is zero. It indicates that the forces are balanced in magnitude, but we need to determine the direction of A.
Since the magnitudes are balanced, we can express this in terms of a vector equation:
0 = A + B + C
To find the direction of A, we can rearrange the equation:
A = -(B + C)
Since B and C are known, we can substitute their values:
A = -(7 kN + 9 kN)
A = -(16 kN)
So, the direction of force A is opposite to the sum of forces B and C, with a magnitude of 16 kN.
Therefore, the direction of force A (F) for the particle to be in equilibrium is 16 kN
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The mix proportion (without adjustments) by weight (SSD) is for concrete mix designed according to ACI 211. The fresh concrete density was 2370 kg/m3 and w/c=0.4. The content of fine aggregate (SSD) is equal to 600 kg per cubic meter and entrapped air is 2%. The specific gravity for .coarse and fine aggregates is 2.67 and 2.65 respectively 1:2.89 3.86 O 1: 1.27:2.35 O 1:1.85: 2.73 O 1: 2.31: 3.37 O
Answer: the mix proportion (without adjustments) by weight (SSD) for the concrete mix designed according to ACI 211 is not directly provided. It requires additional information such as the weight of water and the desired cement content to determine the mix proportion accurately.
The mix proportion (without adjustments) by weight (SSD) for the concrete mix designed according to ACI 211 can be determined using the given information.
Step 1: Calculate the absolute volume of fine aggregate:
Absolute volume of fine aggregate = (content of fine aggregate in kg per cubic meter) / (density of fine aggregate in kg/m3)
Absolute volume of fine aggregate = 600 kg/m3 / 2370 kg/m3
Absolute volume of fine aggregate = 0.253
Step 2: Calculate the absolute volume of entrapped air:
Absolute volume of entrapped air = (volume of entrapped air in %) / 100
Absolute volume of entrapped air = 2% / 100
Absolute volume of entrapped air = 0.02
Step 3: Calculate the absolute volume of coarse aggregate:
Absolute volume of coarse aggregate = 1 - (w/c + absolute volume of fine aggregate + absolute volume of entrapped air)
Absolute volume of coarse aggregate = 1 - (0.4 + 0.253 + 0.02)
Absolute volume of coarse aggregate = 0.327
Step 4: Calculate the weight of fine aggregate:
Weight of fine aggregate = (absolute volume of fine aggregate) * (density of fine aggregate)
Weight of fine aggregate = 0.253 * 2370 kg/m3
Weight of fine aggregate = 600 kg
Step 5: Calculate the weight of coarse aggregate:
Weight of coarse aggregate = (absolute volume of coarse aggregate) * (density of coarse aggregate)
Weight of coarse aggregate = 0.327 * (density of coarse aggregate)
Weight of coarse aggregate = 0.327 * (2.67 * 1000) kg/m3
Weight of coarse aggregate = 878.7 kg
Step 6: Calculate the weight of water:
Weight of water = (w/c) * (weight of cement)
Weight of water = 0.4 * (weight of cement)
Step 7: Calculate the weight of cement:
Weight of cement = (weight of water) / (w/c)
Weight of cement = (weight of water) / 0.4
Based on the given information, the mix proportion (without adjustments) by weight (SSD) for the concrete mix designed according to ACI 211 is not directly provided. It requires additional information such as the weight of water and the desired cement content to determine the mix proportion accurately.
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Is fed gasoline mixture and coloring to the distillation tower it contains (40%)Gasoline we want to separate To get the result of its concentration(90%) gasoline and the remainder contains(10%gasoline )If you know that this mixture enters the tower at its boiling point If you know that this mixture enters the tower at its boiling point(3)And the equilibrium relationship is as follows
X:0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Y:0.22 0.38 0.51 0.63 0.7 0.76 0.85 0.91 1.0
Answer the following questions:
How many theoretical trays?
The efficiency of the tower if you know that the real trays are equal to (5)trays ?
Feed tray number ?
1. The number of theoretical trays is 9.
2. The efficiency of the tower is 1.8.
3. The feed tray number is 3.
Based on the given information, let's break down the questions one by one:
1. To determine the number of theoretical trays in the distillation tower, we can use the equilibrium relationship between the liquid phase composition (Y) and the vapor phase composition (X). The equilibrium data given in the question shows the relationship between X and Y at various stages of the distillation process.
By examining the equilibrium data, we can see that as X increases from 0.1 to 0.9, Y increases from 0.22 to 1.0. However, when X reaches 1.0, Y also reaches 1.0. This indicates that the mixture has achieved complete separation.
Therefore, the number of theoretical trays required can be determined by counting the number of stages from X = 0.1 to X = 1.0. In this case, there are 9 stages or theoretical trays.
2. The efficiency of the distillation tower can be calculated by dividing the number of theoretical trays by the number of actual trays. In this case, we are given that the number of actual trays is 5.
Efficiency = Number of theoretical trays / Number of actual trays
Efficiency = 9 / 5 = 1.8
Therefore, the efficiency of the tower is 1.8.
3. The feed tray is the tray at which the mixture enters the distillation tower. In this case, it is given that the mixture enters at its boiling point, which is tray number 3.
So, the feed tray number is 3.
To summarize:
1. The number of theoretical trays is 9.
2. The efficiency of the tower is 1.8.
3. The feed tray number is 3.
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Engineer A worked for Engineer B. On November 15, 1982 Engineer B notified Engineer A that Engineer B was going to terminate Engineer A because of lack of work. Engineer A thereupon notified clients of Engineer B that Engineer A was planning to start another engineering firm and would appreciate being considered for future work. Meanwhile, Engineer A continued to work for Engineer B for several additional months after the November termination notice. During that period, Engineer B distributed a previously printed brochure listing Engineer A as one of Engineer B's key employees, and continued to use the previously printed brochure with Engineer A's name in it well after Engineer B did in fact terminate Engineer A. Question: 1. Was it ethical for Engineer A to notify clients of Engineer B that Engineer A was planning to start a firm and would appreciate being considered for future work while still in the employ of Engineer B?
It is generally considered unethical for Engineer A to notify clients of Engineer B about their plans to start another engineering firm while still being employed by Engineer B.
Engineer A's actions of notifying clients of Engineer B while still employed can be seen as unethical. Here's a step-by-step explanation:
1. As an employee of Engineer B, Engineer A has a duty of loyalty and confidentiality to their employer. This means that Engineer A should prioritize the interests of Engineer B and not engage in activities that could potentially harm the company.
2. By notifying clients of Engineer B about their plans to start another engineering firm, Engineer A is essentially soliciting business while still being employed by Engineer B. This can be seen as a breach of loyalty and a conflict of interest.
3. Engineer A's actions could potentially harm Engineer B's business by diverting clients and future work opportunities away from Engineer B. This is particularly problematic if Engineer A uses their position at Engineer B to gain an unfair advantage in securing clients for their new firm.
4. It is generally considered ethical for employees to refrain from engaging in activities that could harm their current employer until they have officially left the company. This includes soliciting clients and promoting personal business ventures.
5. Engineer A could have chosen to wait until after their employment with Engineer B ended to inform clients about their new engineering firm. This would have avoided any potential conflicts of interest and upheld their ethical responsibilities as an employee.
In summary, it is generally considered unethical for Engineer A to notify clients of Engineer B about their plans to start another engineering firm while still being employed by Engineer B. Engineer A should have waited until after their employment ended to pursue business opportunities for their new firm.
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What is the value of a in the equation 3a+ b=54 when B=9?
The answer is:
a = 15
Work/explanation:
Plug in 9 for B :
[tex]\sf{3a + b =54}[/tex]
[tex]\sf{3a + 9 =54}[/tex]
Subtract 9 from each side:
[tex]\sf{3a=45}[/tex]
Divide each side by 3:
[tex]\sf{a=15}[/tex]
Therefore, the answer is a = 15.Problem 2. Find the center of mass of a uniform mass distribution on the 2-dimensional region in the Cartesian plane bounded by the curves y =√1-a², y=0, x=0, x= 1.
The center of mass of the uniform mass distribution on the given 2-dimensional region is at (1/2, a/3), where 'a' is the length of the interval on the y-axis.
To find the center of mass, we need to calculate the x-coordinate and y-coordinate of the center of mass separately. The x-coordinate is obtained by integrating x multiplied by the mass distribution function over the region and dividing it by the total mass. In this case, the total mass is the length of the interval on the x-axis, which is 1.
The y-coordinate of the center of mass is obtained by integrating y multiplied by the mass distribution function over the region and dividing it by the total mass. The mass distribution function is constant, so it can be taken out of the integral. Integrating y over the given region gives the area of the region, which is 1/2 * a.
Thus, the x-coordinate of the center of mass is (1/2) * (1/1) = 1/2, and the y-coordinate is (1/2 * a) / (1/1) = a/2. Therefore, the center of mass is located at (1/2, a/2).
Please note that in the original question, there is a typo in the equation for the curve. It should be y = √(1 - x²), not y = √(1 - a²).
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If 9.67 moles of phosphorus reacts with oxygen according to the balanced chemical equation below, how many grams of oxygen are needed for a complete reaction? 4P + 5O2 --> 2P2O5
The number of grams of oxygen required for the complete reaction of 9.67 moles of phosphorus is approximately 781.6 grams.
According to the balanced chemical equation:
4P + 5O2 → 2P2O5
The stoichiometric ratio between phosphorus and oxygen is 4:5. This means that for every 4 moles of phosphorus, 5 moles of oxygen are required to completely react.
Given that we have 9.67 moles of phosphorus, we can set up a proportion to calculate the moles of oxygen required:
4 moles of phosphorus / 5 moles of oxygen = 9.67 moles of phosphorus / X moles of oxygen
Solving for X, we find:
X = (5 moles of oxygen * 9.67 moles of phosphorus) / 4 moles of phosphorus
Now we can convert moles of oxygen to grams using the molar mass of oxygen (O2) which is approximately 32 g/mol:
Grams of oxygen = X moles of oxygen * molar mass of oxygen
By plugging in the calculated value of X, we can determine the grams of oxygen required for the complete reaction.
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A company wants to retrofit their plant with a baghouse, meaning that space is limited. Particle control efficiency of 95% must be achieved. Would you recommend a shaker, reverse air, or pulse jet baghouse?
The recommended baghouse type that can be used to retrofit a plant limited in space and needs to achieve a particle control efficiency of 95% is a pulse jet baghouse.
In order to recommend a baghouse type to retrofit a plant that is limited in space and needs to achieve particle control efficiency of 95%, let us first look at the baghouse options available and their efficiency. A baghouse is an air pollution control device that uses fabric filter tubes to remove particulate matter from the air and gases. There are three types of baghouses that can be used: Shaker Baghouse, Reverse Air Baghouse and Pulse Jet Baghouse.
Shaker baghouses are generally smaller than other baghouse designs and have low initial capital costs. The downside of this type of baghouse is that it has the lowest efficiency compared to reverse air and pulse jet baghouses. This means that it may not be able to achieve the required 95% particle control efficiency.
Reverse Air Baghouse is more efficient than the shaker baghouse. The reverse air baghouse features a cleaning system that uses an adjustable fan to pull air through the baghouse, effectively dislodging the collected dust particles. The collected particles are then discharged to a hopper for storage or disposal. This baghouse type can achieve a particle control efficiency of up to 99%.
However, in our case, it is recommended to use a Pulse Jet Baghouse. This type of baghouse is the most efficient and provides the highest level of particle control efficiency of up to 99.9%. Pulse jet baghouses use high-pressure compressed air to pulse the bags, causing the dust to fall into the hopper below. Pulse jet baghouses have lower operating costs than other types of baghouses due to their smaller size, less frequent cleaning cycles, and use of less compressed air.
Therefore, considering the limitation of space and the required particle control efficiency of 95%, pulse jet baghouse is the best recommendation.
Conclusion: The recommended baghouse type that can be used to retrofit a plant limited in space and needs to achieve a particle control efficiency of 95% is a pulse jet baghouse.
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two people share some money in the ratio 3:5. one person gets $75, find out two possible values with the amount of money the other person gets
Answer:
$46.88 and $28.13
Step-by-step explanation:
What is a ratio?A ratio has two or more numbers that symbolize relation to each other. Ratios are used to compare numbers, and you can compare them using division.
To solve a part-part ratio problem, we need to follow these steps:
Find the total number of parts in the ratio by adding the ratio parts together.Divide the given amount by the total number of parts to find the value of one part.Multiply the value of one part by the ratio part that you want to find.If two people share some money in the ratio 3:5 and one person gets $75, you can find out two possible values with the amount of money the other person gets by doing this:
The total number of parts in the ratio is:
3 + 5 = 8The value of one part is:
$75 ÷ 8 = $9.375The amount of money the other person gets is either:
5 × $9.375 = $46.88 (rounded to 2 decimal places)Or:
3 × $9.375 = $28.13 (rounded to 2 decimal places)Therefore the two possible values are $46.88 and $28.13.
Give the electron configuration for the following (must do all 3): a. Te b. Cr c. Zn²+ Select all of the following that canNOT exceed the octet rule OP Kr C F
a. The electron configuration for the element Te is 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁶5s²4d¹⁰5p⁴.b. The electron configuration for the element Cr is 1s²2s²2p⁶3s²3p⁶3d⁵4s¹.c. The electron configuration for the ion Zn²⁺ is 1s²2s²2p⁶3s²3p⁶3d¹⁰.
Te: 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁶5s²4d¹⁰5p⁴Cr: 1s²2s²2p⁶3s²3p⁶3d⁵4s¹Zn²⁺: 1s²2s²2p⁶3s²3p⁶3d¹⁰.
This question is divided into three parts where the electron configurations of three elements are asked.
The electron configuration of the first element which is Te is 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁶5s²4d¹⁰5p⁴.
The electron configuration of the second element which is Cr is 1s²2s²2p⁶3s²3p⁶3d⁵4s¹ and the electron configuration of the third element which is Zn²⁺ is 1s²2s²2p⁶3s²3p⁶3d¹⁰.
Only F canNOT exceed the octet rule.
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At a local college ,four sections of economics was taught during the day cons use what is the probably that she taking a right and two sections are taught at night 85 percent of the day section are taught by Full time faculty 15 percent of the evening sections taught by Economics use what is the probably that she taking a right
The probably that she is taking right class (Type traction)
The probability that she is taking the right class is approximately 0.57, or 57%.
The probability of taking the right class can be calculated by considering the number of day and evening sections and the percentage of full-time faculty teaching during the day.
Let's break down the given information:
- There are four sections of economics taught during the day.
- Two sections are taught at night.
- 85% of the day sections are taught by full-time faculty.
- 15% of the evening sections are taught by economics faculty.
To calculate the probability, we need to determine the likelihood of taking a day class taught by a full-time faculty member.
Step-by-step calculation:
1. Calculate the total number of sections: 4 day sections + 2 evening sections = 6 sections in total.
2. Calculate the number of day sections taught by full-time faculty: 85% of 4 = 0.85 * 4 = 3.4 (round to the nearest whole number)
3. Calculate the total number of sections taught by full-time faculty: 3.4 day sections + 0 evening sections = 3.4 sections (round to the nearest whole number)
Now, we can calculate the probability of taking the right class:
Probability = Number of desired outcomes / Total number of outcomes
Desired outcomes: Taking a day class taught by full-time faculty (3.4 sections)
Total outcomes: Total number of sections (6 sections)
Probability = 3.4 sections / 6 sections
Therefore, the probability that she is taking the right class is approximately 0.57, or 57%.
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Let a sequence (an)n=1,2,3,… satisfy Then, for any n=1,2,3,…, an=(1)×(2)0^n+(3)×(4)(2)>(4).
We can conclude that for any given sequence (an)n=1,2,3,…, the values of the sequence lie in the closed interval [1,4]. For any n=1,2,3,…, an=(1)×(2)0^n+(3)×(4)(2)>(4) satisfies the inequality 1 ≤ an ≤ 4.
Let a sequence (an)n=1,2,3,… satisfy
Then, for any n=1,2,3,…, an=(1)×(2)0^n+(3)×(4)(2)>(4).
The formula for the given sequence is an=(1)×(2)0^n+(3)×(4)(2)>(4).
We can observe that an is a weighted average of the two numbers 2^0 = 1 and 4^1 = 4 i.e, an = (1/4) × (4) + (3/4) × (1)
An equivalent way to express this is an=(3/4)(1)+(1/4)(4)
Using the above representation, we can say that (an) is a convex combination of the numbers 1 and 4.
Hence, we can conclude that for any given sequence (an)n=1,2,3,…, the values of the sequence lie in the closed interval [1,4].
Therefore, for any n=1,2,3,…, an=(1)×(2)0^n+(3)×(4)(2)>(4) satisfies the inequality 1 ≤ an ≤ 4.
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7. What is different about reading volumes on burets from rending volumes on graduated cylinders? 8. What is a "banging drop"? 9. Why should you rinse pipets and burets with the solution they will contain? 10. What equation should you use to calculate the molarity of acetic acid from the titration data?
7. The main difference between reading volumes on burets and reading volumes on graduated cylinders is the precision of the measurements.
8. A "banging drop" is a term used in titration experiments. It refers to a sudden, sharp change in the color of the solution being titrated.
9. It is important to rinse pipets and burets with the solution they will contain in order to ensure accurate measurements and prevent contamination.
10. The equation used to calculate the molarity of acetic acid from titration data depends on the reaction being carried out and the stoichiometry of the reaction.
7.Burets are typically used in titrations, where the volume needs to be measured very accurately. Burets have a smaller scale and a finer graduation, allowing for more precise measurements compared to graduated cylinders.
8.This change occurs when the titrant is added in excess and reacts with the indicator, causing a noticeable change in the color of the solution.
9. Rinsing removes any residual substances or impurities that may be present in the pipet or buret. By rinsing with the solution to be used, any remaining substances are replaced with the solution, ensuring that only the desired solution is present for accurate measurements.
10. Generally, the equation will involve the balanced chemical equation for the reaction and the volume of the titrant used. For example, if acetic acid is being titrated with a strong base like sodium hydroxide, the equation would be:
Molarity of acetic acid (CH3COOH) = (Molarity of NaOH) x (Volume of NaOH) / (Volume of acetic acid)
The exact equation may vary depending on the specific titration and the reaction being studied.
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Determine the pipe diameters on the drive line if Q design = 500 GPM (use the Darcy-Weisbach method). Determine the dimensions of the regulating tank. Also, calculate the pump power (Efficiency=70%, depth 80 ft); take into account a calculated safety factor within your pump TDH calculations. The pressure at the discharge point is 5 m. The friction factor for PVC is 0.016, and for steel it is 0.022.
The pipe diameters on the drive line using the Darcy-Weisbach method are
D_pvc = 3.18 inches and D_steel = 2.98 inches.
The given problem deals with the determination of the pipe diameters on the drive line using the Darcy-Weisbach method, calculating the dimensions of the regulating tank, and calculating the pump power by taking into account a calculated safety factor within your pump TDH calculations.
Let us solve the problem step by step:Given Data:
Flow Rate, Q design = 500 GPM
Pressure at the discharge point, P = 5 m
Efficiency of the pump, η = 70%Depth, h = 80 ft
Friction factor for PVC, f_pvc = 0.016
Friction factor for Steel, f_steel = 0.022.
Therefore,
The dimensions of the regulating tank are L = 79.7 ft.
The Pump Power is P = 170.32 HP.
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Navier Stokes For Blood Clot region - Find out Velocity Profile and Net Momentum loss
Navier Stokes For Blood Clot region - Velocity Profile and Net Momentum loss.
The Navier-Stokes equation is a set of equations in fluid mechanics that represents the conservation of mass, momentum, and energy. It's a complicated set of nonlinear partial differential equations that describe fluid motion in three dimensions. The flow of blood is a complex fluid flow that is affected by numerous factors, including flow velocity, blood vessel wall properties, and fluid viscosity.
To investigate blood flow, the Navier-Stokes equation may be used. The velocity profile and net momentum loss are then determined using the Navier-Stokes equation. The following is the detailed answer for this question:Velocity Profile:Velocity is a vector quantity that represents the rate of motion in a particular direction. Blood flow velocity is a critical indicator of vascular health.
The velocity profile in the Navier-Stokes equation is determined by determining the velocity at various points in a given fluid. This is accomplished by solving a set of differential equations that take into account the fluid's viscosity, density, and other physical properties.Net Momentum Loss:When a fluid flows through a blood vessel, it exerts a force on the vessel walls. This is referred to as a momentum transfer.
The momentum transfer rate, which is the rate at which momentum is transferred to the vessel walls, is determined using the Navier-Stokes equation. The momentum transfer rate is determined by integrating the fluid's momentum flux over the vessel's cross-sectional area. The net momentum loss can be calculated by subtracting the momentum transfer rate from the initial momentum of the fluid.
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What is the difference between emulsion polymerization and
interfacial polymerization?
Emulsion polymerization and interfacial polymerization are two methods of polymerization. Here are the differences between the two methods:Emulsion PolymerizationEmulsion polymerization is a type of free-radical polymerization that involves a water-soluble initiator. It occurs when monomers are dispersed in water in the presence of a surfactant and a water-soluble initiator that decomposes into free radicals, initiating the polymerization process.
Emulsion polymerization produces waterborne polymers that are widely used in paints, adhesives, and other applications.Emulsion polymerization is advantageous in that it requires less energy than other polymerization methods, and it produces polymers that are easier to purify and handle. However, it can be difficult to control the particle size and shape of the polymer that is produced.
Interfacial Polymerization: Interfacial polymerization involves the reaction of two different monomers, one dissolved in an aqueous solution and the other in an organic solvent. The two monomers are brought into contact at an interface between the two solvents, where they react to form a polymer.Interfacial polymerization is useful for producing polymers with different chemical properties and structures. It is also useful for creating polymer films and coatings.
However, it requires more energy than emulsion polymerization and produces more waste.
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Commercial grade HNO3 solutions in water are
typically 70% (by mass). The solution has a density of 1.42 g/mL.
How many grams of HNO3 are in 80 mL of this
solution?
A.56 g
B. 80 g
C. 39 g
D. 162 g
The grams of HNO3 in 80 mL of the 70% HNO3 solution is approximately 80 g.
To calculate the grams of HNO3 in 80 mL of a 70% (by mass) HNO3 solution, we can follow these steps:
Step 1: Convert the volume of the solution to grams.
Density = 1.42 g/mL
Volume of solution = 80 mL
Mass of solution = Volume of solution × Density = 80 mL × 1.42 g/mL
= 113.6 g
Step 2: Calculate the mass of HNO3 in the solution.
Percentage concentration of HNO3 = 70%
Mass of HNO3 = Mass of solution × Percentage concentration
= 113.6 g × 70%
= 79.52 g
Step 3: Round the answer to the nearest whole number.
Rounding 79.52 g to the nearest whole number, we get 80 g.
Therefore: The grams of HNO3 in 80 mL of the 70% HNO3 solution is approximately 80 g.
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Find the following derivatives. Zg and z₁, where z=e 9x+y x=2st, and y = 3s + 2t =9e9x+y əx (Type an expression using x and y as the variables.) əx ds (Type an expression usings and t as the variables.) dz =/e4x+y ду (Type an expression using x and y as the variables.) 3 ds (Type an expression using s and t as the variables.) x at (Type an expression using s and t as the variables.) dy 2 dt (Type an expression using s and t as the variables.) Zs= (Type an expression usings and t as the variables.) Z₁ = (Type an expression using s and t as the variables.)
The following derivatives. z and Z₁, where z = 6x + 3y, x = 6st, and y = 4s + 9t, the value of Zs =0
Here, we have,
To find the derivative of z with respect to s and t, we can use the chain rule.
Let's start by finding ∂z/∂s:
z = 6x + 3y
Substituting x = 6st and y = 4s + 9t:
z = 6(6st) + 3(4s + 9t)
z = 36st + 12s + 27t
Now, differentiating z with respect to s:
∂z/∂s = 36t + 12
Next, let's find ∂z/∂t:
z = 6x + 3y
Substituting x = 6st and y = 4s + 9t:
z = 6(6st) + 3(4s + 9t)
z = 36st + 12s + 27t
Now, differentiating z with respect to t:
∂z/∂t = 36s + 27
So, the derivatives are:
∂z/∂s = 36t + 12
∂z/∂t = 36s + 27
Now, let's find Zs. We have the equation Z = 4s = 0,
which implies that 4s = 0.
To solve for s, we divide both sides by 4:
4s/4 = 0/4
s = 0
Therefore, Zs = 0.
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complete question:
Find the following derivatives. z and Z₁, where z = 6x + 3y, x = 6st, and y = 4s + 9t Zs = (Type an expression using s and t as the variables.) 4=0 (Type an expression using s and t as the variables
A simple T-beam with bf=600mm h=500mm hf=100mm, bw=300mm with a span of 3m,
reinforced by 5-20mm diameter rebar for tension, 2-20mm diameter rebar for
compression is to carry a uniform dead load of 20kN/m and uniform live load of
10kN/m. Assuming fe'=21Mpa, fy=415Mpa, d'=60mm, cc=40m and stirrups= 10mm,
Calculate the cracking moment:
The cracking moment of the T-beam is approximately 1.21 x 10^6 Nmm.
To calculate the cracking moment of a T-beam, we need to consider the dimensions and reinforcement of the beam, as well as the loads it will be subjected to.
Given:
- bf = 600mm (width of the flange)
- h = 500mm (overall height of the beam)
- hf = 100mm (height of the flange)
- bw = 300mm (width of the web)
- Span = 3m
- Reinforcement: 5-20mm diameter rebar for tension, 2-20mm diameter rebar for compression
- Dead load = 20kN/m
- Live load = 10kN/m
- fe' = 21MPa (characteristic strength of concrete)
- fy = 415MPa (yield strength of reinforcement)
- d' = 60mm (effective depth)
- cc = 40mm (clear cover)
- Stirrups = 10mm
Step 1: Calculate the area of the reinforcement for tension and compression.
- Area of reinforcement for tension: As = (π/4) x (5mm)^2 x number of bars
- Area of reinforcement for compression: Ac = (π/4) x (2mm)^2 x number of bars
Step 2: Calculate the effective depth (d) and the lever arm (a).
- Effective depth (d): d = h - cc - (bar diameter/2) = 500mm - 40mm - (20mm/2) = 460mm
- Lever arm (a): a = d - (hf/2) = 460mm - (100mm/2) = 410mm
Step 3: Calculate the moment of inertia (I).
- Moment of inertia (I): I = (bw x hf^3)/12 + (bf x (h - hf)^3)/12
Step 4: Calculate the cracking moment (Mcr).
- Cracking moment (Mcr): Mcr = (fe' x I)/(d - a)
Let's plug in the given values and calculate the cracking moment:
Step 1:
- Area of reinforcement for tension: As = (π/4) x (20mm)^2 x 5 = 1570mm^2
- Area of reinforcement for compression: Ac = (π/4) x (20mm)^2 x 2 = 628mm^2
Step 2:
- Effective depth (d): d = 500mm - 40mm - (20mm/2) = 460mm
- Lever arm (a): a = 460mm - (100mm/2) = 410mm
Step 3:
- Moment of inertia (I): I = (300mm x 100mm^3)/12 + (600mm x (500mm - 100mm)^3)/12
= 8333333.33mm^4
Step 4:
- Cracking moment (Mcr): Mcr = (21MPa x 8333333.33mm^4)/(460mm - 410mm)
= 1.21 x 10^6 Nmm
Therefore, the cracking moment of the T-beam is approximately 1.21 x 10^6 Nmm.
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Question 2 If 15 m³/s of water flows down a spillway onto a horizontal floor of 3m wide and upstream depth of Im with a velocity of 5 m/s, determine: i. The downstream depth required to cause a hydraulic jump. ii. Height of hydraulic jump. iii. The loss in energy head. iv. The losses in power by the jump. V. The type of flow after the jump.
The losses in power by the jump is -15546.1 W.V. Type of flow after the jump: After the hydraulic jump, the type of flow is subcritical flow.
To determine the characteristics of the hydraulic jump, we can use the principles of conservation of mass and energy.
Given the following information:
Flow rate (Q) = 15 m³/s
Width of the floor (b) = 3 m
Upstream depth (h₁) = Im (unknown)
Upstream velocity (V₁) = 5 m/s
i). The downstream depth required to cause a hydraulic jump:
To determine the downstream depth (h₂),
we can use the energy equation:
h₂ = h₁ + (V₁² / (2g)) - (Q² / (2g × b² × h₁²))
Where g is the acceleration due to gravity.
ii). Height of the hydraulic jump:
The height of the hydraulic jump (H) can be calculated using the specific energy equation:
[tex]H=(V_1^2 / (2g)) * ((1 + (Q / (b * V_1 * h_1)))^{(2/3)} - 1)[/tex]
iii). The loss in energy head:
The loss in energy head (ΔE) can be calculated by subtracting the specific energy at the hydraulic jump (E₂) from the specific energy at the upstream condition (E₁):
ΔE = E₁ - E₂
ΔE = (V₁² / (2g)) - (V₂² / (2g)) + g × (h₁ - h₂)
iv). The losses in power by the jump:
The power loss (Ploss) can be calculated by multiplying the loss in energy head (ΔE) by the flow rate (Q):
Ploss = ΔE × Q
The losses in power by the jump is -15546.1 W.V.
v). The type of flow after the jump:
The type of flow after the jump can be determined based on the Froude number (Fr₂) calculated using the downstream depth (h₂) and downstream velocity (V₂):
Fr₂ = V₂ / √(g × h₂)
If Fr₂ < 1, the flow is subcritical (tranquil flow).
If Fr₂ > 1, the flow is supercritical (rapid flow).
Type of flow after the jump: After the hydraulic jump, the type of flow is subcritical flow.
Therefore, the losses in power by the jump is -15546.1 W.V. Type of flow after the jump: After the hydraulic jump, the type of flow is subcritical flow.
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Select the lightest available W section of Gr. 50 steel for a beam that is simply supported on the left end and a fixed support on the right end of a 10 meter span. The member supports a service dead load of 3kN/m, including its self weight and a service live load of 4KN/m. The nominal depth of the beam is provided at the ends and 1/3 point of the span. Use cb equivalent to 1.0.
That W100x15 is the lightest available W-section of Gr. 50 steel which can be used for the given beam. The lightest W-section with a Z-value equal to or greater than the required value of 21,875 cm³ is W100x15 which has a b/d ratio of 12.04/9.15.
Service Dead Load = 3kN/m,
including self weight service
Live Load = 4kN/mLength of span (L) = 10mNominal depth of beam provided at ends and 1/3 point of span cb equivalent to 1.0
.Solution:
From the given data, the service load acting on the beam will be equal to:
(3 + 4) kN/m = 7 kN/mTotal Load on the beam,
W = 7 kN/m x 10 m = 70 kN/m
For a beam which is simply supported at one end and fixed at the other end, the maximum bending moment will occur at the fixed end and its value will be:Max Bending Moment,
M = WL/8 = 70 x 10 x 10 / 8 = 875 kN-m
Now, we know that the moment of inertia (I) of a W-section of given size is constant for all the sections having the same size.Hence, the selection of the lightest available W-section depends only on the section modulus (Z). The section modulus is given as:
Z = (1/6) x b x d²
where b = width of the beam and
d = depth of the beam.For maximum efficiency,
the section with the least weight would have the least value of b/d ratio. Hence, we select the W-section with the smallest possible b/d ratio and which also has a Z-value equal to or greater than the required value of the section modulus.The required section modulus of the beam is calculated as follows:
Section modulus,
Z = (M/S) = (σ_y × M) / cbwhere
S = allowable stress (σ_y)
cb = L / 10We can assume that the allowable stress σ_y is equal to 250 MPa for Gr. 50 steel.
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12. Lucy has a bag of Skittles with 3 cherry, 5 lime, 4 grape, and 8 orange
Skittles remaining. She chooses a Skittle, eats it, and then chooses
another. What is the probability she get cherry and then lime?
A tank contains 1600 L of pure water. Solution that contains 0.02 kg of sugar per liter enters the tank at the rate 8 L/min, and is thoroughly mixed into it. The new solution drains out of the tank at the same rate. (a) How much sugar is in the tank at the begining? y(0) (kg) (b) Find the amount of sugar after t minutes. y(t) (kg) (c) As t becomes large, what value is y(t) approaching? In other words, calculate the following limit. lim y(t) t→[infinity] (kg)
The volume of the tank remains constant, the rate of change of the amount of sugar in the tank is zero. Therefore, the amount of sugar in the tank remains constant over time, and y(t) = y(0) = 0.16 kg.
Let's solve the problem step by step:
(a) To find the amount of sugar in the tank at the beginning, we can calculate the initial amount of sugar when 8 liters of the solution enter the tank. The concentration of sugar in the solution is 0.02 kg/L, and 8 liters of the solution enter per minute. Therefore, the initial amount of sugar in the tank is:
y(0) = 0.02 kg/L * 8 L = 0.16 kg
So, at the beginning, there are 0.16 kg of sugar in the tank.
(b) To find the amount of sugar after t minutes, we need to consider the rate at which the solution enters and drains from the tank. For every minute, 8 liters of the solution enter and drain from the tank, resulting in a constant volume of 1600 liters in the tank.
The amount of sugar entering the tank per minute is:
0.02 kg/L * 8 L = 0.16 kg/min
The amount of sugar leaving the tank per minute is also 0.16 kg/min since the concentration remains constant in the tank.
Since the volume of the tank remains constant, the rate of change of the amount of sugar in the tank is zero. Therefore, the amount of sugar in the tank remains constant over time, and y(t) = y(0) = 0.16 kg.
(c) As t becomes large, the value of y(t) approaches the initial amount of sugar in the tank, which is y(0) = 0.16 kg. Therefore, the limit of y(t) as t approaches infinity is:
lim y(t) as t→∞ = 0.16 kg.
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Explain Fire Barriers and how they differ from Fire
Partitions?
Fire barriers and fire partitions are both used in building design to prevent the spread of fire. However, there are some differences between the two that are important to understand.
Fire partitions are used to divide a building into smaller fire compartments, and they have a fire resistance rating of at least one hour. They are designed to keep smoke and flames from spreading from one compartment to another.
Fire barriers, on the other hand, are designed to prevent the spread of fire and smoke between different types of occupancies (e.g. between a storage facility and an office building). Fire barriers are usually required to have a fire resistance rating of two or three hours.
Fire barriers and partitions are both required to have fire-resistant walls, floors, and ceilings. However, fire barriers are required to have additional features, such as fire doors and smoke dampers, to ensure that they are effective at preventing the spread of fire.
Fire barriers must also be tested and certified by a third-party testing agency to ensure that they meet the required fire resistance ratings.
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Show that if E is L-non-measurable, then ∃ a proper subset B of E such that 0<μ∗(B)<[infinity].
If E is L-non-measurable, then there exists a proper subset B of E such that 0 < μ∗(B) < ∞.
In measure theory, a set E is said to be L-non-measurable if it does not have a well-defined measure. This means that there is no consistent way to assign a non-negative real number to every subset of E that satisfies certain properties of a measure.
Now, if E is L-non-measurable, it implies that the measure μ∗(E) of E is either undefined or infinite. In either case, we can find a proper subset B of E such that the measure of B, denoted by μ∗(B), is strictly greater than 0 but less than infinity.
To see why this is true, consider the following: Since E is L-non-measurable, there is no well-defined measure on E. This means that there are subsets of E that cannot be assigned a measure, including some subsets that have positive "size" or "content." We can then choose one such subset B that has a positive "size" according to an informal notion of size or content.
By construction, B is a proper subset of E, meaning it is not equal to E itself. Moreover, since B has positive "size," we can conclude that 0 < μ∗(B). Additionally, because B is a proper subset of E, it cannot have the same "size" as E, which implies that μ∗(B) is strictly less than infinity.
In summary, if E is L-non-measurable, we can always find a proper subset B of E such that 0 < μ∗(B) < ∞.
In measure theory, the concept of measurability is fundamental in defining measures. Measurable sets are those for which a measure can be assigned in a consistent and well-defined manner. However, there exist sets that are not measurable, known as non-measurable sets.
The existence of non-measurable sets relies on the Axiom of Choice, a principle in set theory that allows for the selection of an element from an arbitrary collection of sets. It is through this axiom that we can construct non-measurable sets, which defy a well-defined measure.
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In your opinion, what will the resultant phase of a pure substance be when its saturated liquid form is heated at a constant specific volume? Explain.
When a saturated liquid form of a pure substance is heated at a constant specific volume, the resultant phase of the substance will be its saturated vapor form.
This is because, at constant specific volume, the substance will undergo a phase change from liquid to vapor as it is heated up. A pure substance is one that is made up of only one type of molecule. It can exist in different phases, including solid, liquid, and gas/vapor. The phase that the substance exists in depends on factors such as temperature and pressure. At a given pressure, if a pure substance is heated up while being kept at a constant specific volume (i.e., its volume is not allowed to change), it will eventually reach a temperature at which it undergoes a phase change from liquid to vapor.
This is because the substance's saturated liquid form can only exist at a certain temperature and pressure combination, and if the temperature is increased beyond this point, the liquid will turn into vapor. Thus, the resultant phase of the substance will be its saturated vapor form.
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Symbolize the following 15 English sentences in the notation we have learned.
1) All students are rich. (Sx: x is a student, Rx: x is rich)
2) Some students can drive. (Sx: x is a student, Dx: x can drive)
3) No student hates logic. (Sx: x is a student, Hx: x hates logic)
4) Some students don’t like History. (Sx: x is a student, Hx: x likes history)
5) Every scoundrel is unhappy. (Sx: x is a scoundrel, Hx: x is happy)
6) Some games are not fun. (Gx: x is a game, Fx: x is fun)
7) No one who is honest is a banker. (Px: x is a person, Hx: is honest, Bx: x is a banker)
8) Some old cars are not fashionable. (Ox: x is old, Cx: x is a car, Fx: x is fashionable)
9) No student is neither clever nor ambitious. (Sx: x is a student, Cx: x is clever, Ax: x is ambitious)
10) Only members are allowed inside without paying. (Mx: x is a member, Ax: x is allowed inside, Px: x has to pay)
11) Unless every professor is friendly, no student is happy. (Px: x is a professor, Fx: x is friendly, Sx: x is a student, Hx: xis happy,)
12) Some students understand every teacher. (Sx: x is a student, Tx: x is a teacher, Uxy: x understands y)
13) Not every doctor likes some of their patients. (Dx: x is a doctor, Pxy: x is a patient of y, Lxy: x likes y)
14) Some students listen to every one of their professors. (Sx: x is a student, Pxy: x is a professor of y, Lxy: x listens to y)
15) Every student who doesn’t read every book will not get any high grades. (Sx: x is a student, Bx: x is a book, Gx: x is a grade, Hx: x is high, Gxy: x gets y, Rxy: x reads y)
To symbolize the given English sentences in logical notation, the following symbols:
Sx: x is a student
Rx: x is rich
Dx: x can drive
Hx: x hates logic
Lxy: x likes y
Gx: x is a game
Fx: x is fun
Px: x is a person
Bx: x is a banker
Ox: x is old
Cx: x is a car
Fx: x is fashionable
Ax: x is ambitious
Mx: x is a member
Ax: x is allowed inside
Px: x has to pay
Px: x is a professor
Fx: x is friendly
Sx: x is a student
Hx: x is happy
Tx: x is a teacher
Uxy: x understands y
Dx: x is a doctor
Pxy: x is a patient of y
Lxy: x likes y
Bx: x is a book
Gx: x is a grade
Hx: x is high
Gxy: x gets y
Rxy: x reads y
All students are rich.
Symbolization: ∀x (Sx → Rx)
Some students can drive.
Symbolization: ∃x (Sx ∧ Dx)
No student hates logic.
Symbolization: ∀x (Sx → ¬Hx)
Some students don't like History.
Symbolization: ∃x (Sx ∧ ¬Hx)
Every scoundrel is unhappy.
Symbolization: ∀x (Sx → ¬Hx)
Some games are not fun.
Symbolization: ∃x (Gx ∧ ¬Fx)
No one who is honest is a banker.
Symbolization: ∀x (Px ∧ Hx → ¬Bx)
Some old cars are not fashionable.
Symbolization: ∃x (Cx ∧ Ox ∧ ¬Fx)
No student is neither clever nor ambitious.
Symbolization: ∀x (Sx → ¬Cx ∧ ¬Ax)
Only members are allowed inside without paying.
Symbolization: ∀x (Ax → Mx → ¬Px)
Unless every professor is friendly, no student is happy.
Symbolization: ∀x (Px → Fx → Sx → ¬Hx)
Some students understand every teacher.
Symbolization: ∃x (Sx ∧ ∀y (Ty → Uxy))
Not every doctor likes some of their patients.
Symbolization: ∀x (Dx → ∃y (Pxy → ¬Lxy))
Some students listen to every one of their professors.
Symbolization: ∃x (Sx ∧ ∀y (Pxy → Lxy))
Every student who doesn’t read every book will not get any high grades.
Symbolization: ∀x (Sx → ∀y (Bx → ¬Rxy → ¬Gy))
In this symbolic notation, quantifiers (∀ for "for all" and ∃ for "there exists") are used to express universal and existential statements, and logical connectives (¬ for "not," ∧ for "and," → for "implies") are used to combine these statements logically.
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The center of mass of a composite body: Is calculated as the sum of the product of the mass of each figure involved in the composite body divided by the total mass of the object. Requires integration for its calculation in all cases. Is calculated as the sum of the mass of each figure involved in the composite body multiplied by the distance of the centroid of that figure from a coordinate axis established on the object. Is the same as the center of gravity of the composite object.
The correct statement regarding the center of mass of a composite body is that it is calculated as the sum of the product of the mass of each figure involved divided by the total mass of the object.
The centre of mass of a composite body is determined by multiplying the total mass of the object by the sum of the products of the masses of all the figures that make up the composite body. Since it may be calculated by straightforward addition and division, this method does not always require integration.
The centre of mass is determined by adding the masses of all the individual components of the composite body and dividing the result by the distance between each component's centroid and a coordinate axis placed on the item.
The center of mass and the center of gravity of a composite object are not necessarily the same. The center of gravity specifically refers to the point where the entire weight of the object can be considered to act, while the center of mass refers to the average position of the mass distribution. In a uniform gravitational field, the center of gravity coincides with the center of mass, but in other cases, they may differ.
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1.A vegetable oil extractor costing Rs. 1,50,000 with annual operating cost of Rs. 45,000 and an estimated life of 12 years has a salvage value of Rs. 18,000. Alternate oil extractor equipment costs Rs. 54,000 with a life of 6 years has Rs. 6000 junk value and the operating costs are Rs. 75,000 annually. What is the rate of returns for the extra investment if the extractor is replaced.
To calculate the rate of return for the extra investment, we need more information such as the cash inflows from the extractor and the alternate equipment. Without this information, it is not possible to determine the rate of return.
To calculate the rate of return, we would need the cash inflows generated by both the existing extractor and the alternate equipment. Cash inflows could come from the sale of vegetable oil or any other revenue generated by using the equipment. Without these values, we cannot calculate the rate of return.
Additionally, the rate of return calculation would also require the initial investment, salvage value, and the time period considered. In this case, the initial cost and salvage value for the existing extractor are provided, but we still need the initial cost and salvage value for the alternate equipment.
Without the necessary data, it is not possible to determine the rate of return for the extra investment in the extractor replacement.
The calculation of the rate of return for the extra investment in the extractor replacement cannot be determined without knowing the cash inflows from both the existing extractor and the alternate equipment.
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Directions: Solve the following problems using the GRADS-IDEA method and upload your scans or typed responses. 1. During the process of fermentation, glucose breaks down into ethanol and carbon dioxide. a. Write the balanced equation for this reaction. b. Using standard heat of formation values, calculate the heat of reaction if 20 mol of glucose are degraded in this reaction. C. Suppose the reaction does not go to completion. Calculate the heat of reaction if the fractional conversion of glucose is 0.7.
a. The balanced equation is C₆H₁₂O₆ ⇒ 2C₂H₅OH + 2CO₂
b. Heat of reaction is -1378 KJ/mol.
c. Heat of reaction for reaction with conversion 0.7 is -964.6 KJ/mol.
Given that,
a. We have to find the balanced equation for this reaction.
The balance equation for fermentation of glucose is
C₆H₁₂O₆ ⇒ 2C₂H₅OH + 2CO₂
Therefore, The balanced equation is C₆H₁₂O₆ ⇒ 2C₂H₅OH + 2CO₂
b. We have to calculate the heat of reaction if 20 mol of glucose are degraded in this reaction using standard heat of formation values.
Standard heat of formation of Glucose is 1273.3 KJ/mol
Standard heat of formation of Ethanol is 277.6 KJ/mol
Standard heat of formation of Carbon dioxide is 393.5 KJ/mol
Number of mole of glucose are 20 mole
Number of moles of ethanol formed in complete reaction is 2×20 = 40 mole
Number of moles of Carbon Dioxide formed in complete reaction is 2×20 = 40 mole
Heat of reaction = ΔH (products) – ΔH (reactants)
So,
Heat of products is 40 × (-277.6) + 40 × (-393.5) = -26,844 KJ/mol
Heat of reactants is 20 × (-1273.3)= -25,466 KJ/mol
Heat of reaction = -26,844 - (-25,466)= -1378 KJ/mol
Therefore, Heat of reaction is -1378 KJ/mol.
c. Let the reaction does not go to completion.
In the event where the fractional conversion of glucose is 0.7, we must determine the heat of reaction.
The fractional conversion of glucose is 0.7
Number of glucose that will react = 0.7 × 20 = 14 mole
So, only 14 mole of glucose will react. Rest 6 moles would not undergo reaction and there will not be considered.
Number of moles of ethanol formed = 2 × 14= 28 mole
Number of moles of carbon dioxide formed= 28 mole
Now calculation heat of reaction
Heat of products is 28 × (-277.6) + 28 × (-393.5) = -18790.8 KJ/mol
Heat of reactants is 14 × (-1273.3)= -17826.2 KJ/mol
Heat of reaction = -18790.8 - (-17826.2)= -964.6 KJ/mol
Therefore, Heat of reaction for reaction with conversion 0.7 is -964.6 KJ/mol.
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This experiment will allow us to examine how changes in volume affect the pressure of a gas in a container. 1) Circle the correct response: a) To increase the volume of a gas in a container we must [increase; decrease] the surface area of the container. b) There are [the same; fewer] number of molecules in the container when the volume of the container is changed. c) Pressure in force/area. As the volume of the gas increases then the area [increases; decreases] and so the pressure of the gas [increases; decreasesl.
To increase the volume of a gas in a container we must decrease the surface area of the container. There are the same number of molecules in the container when the volume of the container is changed.
Pressure in force/area. As the volume of the gas increases then the area decreases and so the pressure of the gas decreases. To increase the volume of a gas in a container we must decrease the surface area of the container. The volume of a gas in a container increases when the surface area of the container decreases. For instance, when the container's lid is opened, the volume of the gas expands and occupies more space. In order to increase the volume of gas, the surface area must decrease. There are the same number of molecules in the container when the volume of the container is changed.
Changing the volume of a container has no effect on the number of gas molecules in it. The total number of gas molecules remains constant when the volume is increased or decreased. Changing the volume of a gas in a container does not change the number of gas molecules inside it. Pressure in force/area. As the volume of the gas increases then the area decreases and so the pressure of the gas decreases. According to Boyle's Law, the pressure of a gas is inversely proportional to its volume when the temperature is constant. If the volume of a gas is increased, the area decreases, and pressure of the gas decreases. Therefore, when the volume of gas is increased, the pressure of gas decreases.
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Answer:
the correct answers are:
a) Increase
b) The same
c) Decreases
Step-by-step explanation:
a) To increase the volume of a gas in a container we must [increase; decrease] the surface area of the container.
Answer: Increase
b) There are [the same; fewer] number of molecules in the container when the volume of the container is changed.
Answer: The same
c) Pressure is force/area. As the volume of the gas increases, then the area [increases; decreases] and so the pressure of the gas [increases; decreases].
Answer: Decreases
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