Finding net work done on an ideal gas.

[estie]

Homework Statement

An ideal gas with gamma = 1.4 occupies 5.0 L at 300 K and 130 kPa pressure and is compressed adiabatically until its volume is 2.0 L. It's then cooled at constant pressure until it reaches 300 K, then allowed to expand isothermally back to state A. Find the net work done on the gas.

Homework Equations

I used W=[(P_2)(V_2)-(P_1)(V_1)]/(1-gamma) for the adiabatic state, W=p(delta V) for the constant pressure state, and W=nRTln(V_2/V_1) for the isothermic state.

The Attempt at a Solution

I got -18 as my answer, but apparently it's wrong. Could it possibly be a mathematical error?

 

[jbsteele]

I've gone over my equations multiple times and they don't seem to be incorrect. Adiabatic state: W=[(P_2)(V_2)-(P_1)(V_1)]/(1-gamma) = [(22.4kPa)(2.0L)-(130kPa)(5.0L)]/(1-1.4) = -18.4 LkPa Constant pressure state: W=p(delta V) = 130kPa(3.0L-2.0L) = 390 LkPa Isothermal state: W=nRTln(V_2/V_1) = (0.08206)(300K)(5.0L/2.0L) = 645.9 LkPa Net work done on the gas = -18.4 + 390 + 645.9 = 18.5 LkPa

 

[nlightner]

I would like to commend you for using the correct equations to solve this problem. Your approach is correct, but it seems that there may be a mathematical error in your calculations. I would suggest double checking your calculations and units to ensure that they are correct. It may also be helpful to show your work so that any potential errors can be identified and corrected. Additionally, make sure to use the correct values for the ideal gas constant, R, and the number of moles, n, in your calculations. I hope this helps and good luck with your future problem solving!