Why Can Volume Be Used Instead of Specific Volume in PV Diagrams?

[dan28029]

1. Problem Statement

The problem asks to find the net work from one complete cycle A-B-C. Problem 13, starting on page 66 of the slide show here:

https://engineering.purdue.edu/~xe/Files/FE%20Review/Thermo/FEThermoReview2013.pdf

Homework Equations

ideal gas law: PV=mRT
Boyle's Law: W=RTln(v2/v1)

3. Attempt at solution

I understand most of the solution, but on page 67, says that W=R*T*ln(Vb/Va) is equivalent to W=p*Va*ln(Vb/Va), assuming ideal gas and constant mass. I don't understand why you can use volume here instead of specific volume.

From the ideal gas law: PV=mRT and RT=PV/m. So I thought it should be W=p*Va/m*ln(Vb/Va). Why can we eliminate m here?

Thank you!

 

[Chestermiller]

There should be an m in the equation W=R*T*ln(Vb/Va). It should read W=m*R*T*ln(Vb/Va).

 

[rude man]

What's wrong is "W = RT ln(Vb/Va)". It should be W = mRT ln(Vb/Va).
Notice that the wrong formula is never used in the computations.

P.S. why do they put a slash thru the V's?

 

[BOYLANATOR]

One equation for isothermal work is W = m*R*T* ln(Vb/Vb). He has either made a mistake by omitting the number of moles or he has calculated the heat for 1 mole.

 

[dan28029]

Thanks for the responses. Good to know I'm not crazy.

There should be an m in the equation W=R*T*ln(Vb/Va). It should read W=m*R*T*ln(Vb/Va).

In the reference material for the fundamentals of engineering exam, the formula also does not include mass. I guess its a typo. Maybe that's where the author of the presentation got the formula from.

P.S. why do they put a slash thru the V's?

I think it is to differentiate between volume and specific volume. It confused me at first though.