# Question about work done by expanding pressurized gas

In my thermodynamics class, we were shown an equation that gives the work done by expanding pressurized gas given as the integral from v1 to v2 of C/V*dV where C is a constant and v1 and v2 are initial and final volumes respectively. My question has to do with the fact that this is basically the integral of 1/V*dV which implies that as a gas expands to infinity, it will do infinite work which then implies that pressurized gas has infinite potential energy which I know cannot be true. Can anyone explain what is wrong with this logic? I asked the professor, but she just said it had something to do with thermodynamic laws not applying to stuff that goes to infinity.

## Answers and Replies

Hi, JerryG

In my thermodynamics class, we were shown an equation that gives the work done by expanding pressurized gas given as the integral from v1 to v2 of C/V*dV where C is a constant and v1 and v2 are initial and final volumes respectively.

Equation of state for ideal gas PV=NkT stands for your case. P=NkT / V = C /V
As C is a constant, T is constant so the system is in heat bath of constant temperature T. Infinite energy is supplied from heat bath to gas during its infinite expansion.

Regards

Last edited:
Andrew Mason
Science Advisor
Homework Helper
Further to what sweet springs has said: apply the first law:

$$\Delta Q = \Delta U + W = \Delta U + C\ln\frac{V_2}{V_1}$$

The heat flow into the system less the change in internal energy has to equal the work done by the system. There is a limit to the internal energy change. So there can be no limit to the work done only if there is no limit to the heat flow into the system.

AM

Hi I am a new member and this is my first post. I am currently taking an engineering Thermodynamics class and am having some trouble with an assigned problem dealing with air in a piston cylinder.

Process 1-2: Air is compressed PV^n=constant
Process 2-3: Air expands P=constant until V3=V1

given r=5=V1/V2 and T1=300K

determine ratio of the work of expansion to the work of compression in terms of r and n when
n does not equal 1 and when n=1 and evaluate when A)n=1.4 and B)n=1

I had no problem finding Wexp/Wcomp when n does not equal one
(r-1)(n-1) / (1-r^(1-n)) A)3.37

and Wexp/Wcomp when n=1 (r-1)/ln[r] B)2.48

part 2 check answers by finding the actual Wexpansion and Wcompression and forming the the ratios for each case.

my question is given only T1 and V1/V2=5 do I have enough information to actually solve for anything other then the ratio itself in each case?
Ideal gas so PV=mRT and Specific heat equations are what I have been working from and I have a Property Table book which supplies u1 and h1 values.