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.

 

[astrokreng]

I would say that the solution provided in this problem is incorrect. The ideal gas law, which is PV = nRT, should be used to solve for the work in an isothermal process, where n is the number of moles of gas. In this problem, the solution incorrectly uses PA*VA instead of (PA*VA)/n, which is not a valid substitution.

In addition, the problem does not provide information about the number of moles of gas or the mass of the gas, which is necessary to solve for the work in an isothermal process. Without this information, it is impossible to accurately solve for the work in the A-to-B process.

I would recommend bringing this issue to the attention of the review book's publisher or author so that they can correct the mistake and provide a more accurate solution for students preparing for the FE exam. It is important for review materials to be accurate and reliable in order to properly prepare students for their exams.