Reviewing for the FE exam, came across questionable thermo problem.

[jasc15]

Im studying for the Fundamentals of Engineering exam (coming up April 12!) and came across this Thermodynamics problem in my review book.

A gas goes through the following processes:

A to B: isothermal compression
B to C: isochoric compression
C to A: isobaric expansion

P_C = P_A = 1.4bar
V_C = V_B = 0.028m³
The net work during the C-to-A process is W_CA = 10.5kJ

What work is performed in the A-to-B process?

So the work for an isothermal process is RT_A*ln(V_B/V_A), where V_A was previously determined to be 0.103m³.

In the solution to the problem, the RT_A term is replaced with P_A*V_A, where it should be (P_A*V_A)/n from the ideal gas law.

Is this solution wrong? As I see it, this can't be solved without knowing the number of moles of gas (or mass of the gas depending on which R is used). I was unable to get the correct answer, and the solution seems wrong to me.

 

[Mapes]

The solution should have replaced nRT_A with P_AV_A. You don't need to know the amount of gas to solve this problem.

EDIT: I get -18.8 kJ for the work done in the A-to-B process.