# Volume of gas in a thermodynamic cycle.

• merbear
In summary, when finding the volume at point B in the given thermodynamic cycle, it is important to use the correct values for pressure and temperature and double check calculations to ensure accuracy.
merbear

## Homework Statement

A 1 mol sample of an ideal gas for which c'V = 3R/2 follows the closed thermodynamic cycle shown in Fig. 18-36. There are three legs in the cycle: an isothermal expansion, A B; an isobaric compression, B C; and a constant-volume increase in pressure, C A. The temperature during the isothermal leg is 340 K, pA = 1.8 atm, and pB = 1.2 atm. Find each of the following. (a) Va (b) Vb. (See attachment for image - ignore the pressure numbers on the graph and use the numbers given in the problem)

## Homework Equations

Pv=nRT (initial and final)

## The Attempt at a Solution

Pa: V= [1 mol (.08205784 L*atm/k*mol)(340K)]/1.8 atm = 15.499 L = .0155 M^3

Pb: V= [1 mol (.08205784 L*atm/k*mol)(340K)]/`1.2 atm = 23.25 L = .0232 M^3

When I plugged those answers to see if they were right, the first one came up right for the volume at A. But my response for the volume at B came up incorrect. I performed the problem in the same way just changing the numbers, I don't understand why it is incorrect. Any help would be appreciated.

Thank-you

#### Attachments

• 18-36fig-alt 2.gif
1.8 KB · Views: 483
for your post. It seems like you may have made a small calculation error when finding the volume at point B. When plugging in the given values for pB and pC, the volume at B should be 0.0232 m^3, not 0.0235 m^3 as you have calculated. This small difference could be the reason why your answer for Vb is coming up incorrect. I suggest double checking your calculations and making sure you are using the correct values for pressure and temperature at point B. Let me know if this helps or if you have any further questions.

I would first like to commend the student for their attempt at solving the problem and using the appropriate equations. However, I would like to point out that there might be a mistake in the calculation for Vb. In the given problem, it is stated that the pressure at B is 1.2 atm, not 1.8 atm. Therefore, the correct calculation for Vb would be:

Vb = [1 mol (.08205784 L*atm/k*mol)(340K)]/1.2 atm = 28.125 L = 0.0281 M^3

I would suggest double-checking the calculations to ensure accuracy. Additionally, it is always helpful to provide a clear explanation of the steps taken to arrive at the solution, as this can help identify any potential errors.

## 1. What is the definition of volume of gas in a thermodynamic cycle?

The volume of gas in a thermodynamic cycle refers to the amount of space that the gas occupies within a closed system. It is a key factor in determining the behavior of the gas as it undergoes changes in pressure, temperature, and other properties.

## 2. How is the volume of gas calculated in a thermodynamic cycle?

The volume of gas in a thermodynamic cycle can be calculated using the ideal gas law, which states that the volume of a gas is directly proportional to its number of moles, temperature, and inversely proportional to its pressure. This relationship is expressed in the equation V = nRT/P, where V is volume, n is number of moles, R is the gas constant, T is temperature, and P is pressure.

## 3. What is the significance of the volume of gas in a thermodynamic cycle?

The volume of gas plays a crucial role in determining the efficiency and performance of a thermodynamic cycle. It affects the amount of work that can be produced by the system, as well as the heat transfer and overall energy balance.

## 4. How does the volume of gas change in different stages of a thermodynamic cycle?

In a thermodynamic cycle, the volume of gas can change as the gas undergoes different processes such as compression, expansion, and heating. For example, during compression, the volume decreases as the gas is forced into a smaller space, while during expansion, the volume increases as the gas expands into a larger space.

## 5. Can the volume of gas in a thermodynamic cycle be controlled?

Yes, the volume of gas in a thermodynamic cycle can be controlled by adjusting the pressure, temperature, or volume of the system. This is often done in order to optimize the performance of the cycle and achieve specific goals, such as increasing efficiency or maintaining a certain temperature range.

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