Question about work done by expanding pressurized gas

[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. 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.

 

[sweet springs]

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

 

[Andrew Mason]

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

 

[George TM]

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.