# Volume of gas in a thermdynamic cycle

• merbear
Your Name]In summary, the conversation is about a problem involving an ideal gas following a closed thermodynamic cycle. The problem asks for the volume at points A and B, and the user has attempted to solve it but has encountered an error in their calculation for point B. They have asked for help and have been advised to double check their calculations and consider using the ideal gas law. They are also encouraged to seek assistance from a classmate or teacher if needed.
merbear
1. 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)

2. Homework Equations

Pv=nRT (initial and final)

3. 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.gif
1.8 KB · Views: 451

Thank you for sharing your attempt at solving this problem. It appears that you have correctly calculated the volume at point A, but there may be an error in your calculation for point B. I would suggest double checking your calculations and also making sure that you are using the correct units for pressure (atm) and volume (L or m^3).

Additionally, it may be helpful to consider the ideal gas law in your calculations for point B, as the problem states that the gas is ideal. This equation relates pressure, volume, moles, and temperature, and may provide a more accurate answer for point B.

If you are still having trouble, I would recommend seeking assistance from a classmate or your teacher. They may be able to provide additional guidance and clarification.

Best of luck with your calculations!

## 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 a gas takes up in a system during the process of a thermodynamic cycle. It is typically measured in units of liters or cubic meters.

## How is the volume of gas related to the pressure and temperature in a thermodynamic cycle?

In a thermodynamic cycle, the volume of gas is directly proportional to the temperature and inversely proportional to the pressure. This means that as the temperature increases, the volume of gas will also increase, while a decrease in pressure will result in an increase in volume.

## What factors can affect the volume of gas in a thermodynamic cycle?

The volume of gas in a thermodynamic cycle can be affected by a variety of factors, including the amount of gas present, the temperature, the pressure, and any changes in these parameters during the cycle. Additionally, the type of gas and the properties of the container it is in can also impact the volume.

## 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 equal to the number of moles of gas multiplied by the gas constant and the temperature, divided by the pressure. This equation is V=nRT/P, where V is volume, n is the number of moles, R is the gas constant, T is the temperature, and P is the pressure.

## Why is the volume of gas important in thermodynamics?

The volume of gas is an important factor in thermodynamics because it is directly related to the amount of work that can be done by a system. As the gas expands and takes up more volume, it can perform more work. Additionally, changes in volume can also indicate changes in the internal energy and heat transfer of a system, which are important concepts in thermodynamics.

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