Volume of gas in a thermodynamic cycle.

[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

 

[anathema]

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.

 

[Moetasim]

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.