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.

 

[PJC01]

There are a few key concepts that need to be addressed in order to fully understand this question. Firstly, it is important to understand that the equation you were shown in your thermodynamics class is a simplified version of the work done by expanding pressurized gas. In reality, the equation would also include factors such as temperature, pressure, and the number of molecules present. However, for the sake of simplicity, these factors were omitted in the equation you were shown.

Secondly, it is important to understand that the equation you were shown is only applicable for a finite expansion of the gas. As you correctly noted, if the gas were to expand to infinity, the equation would suggest that an infinite amount of work would be done, which is not physically possible. This is because, in reality, the gas will eventually reach a state of equilibrium where the pressure and volume are constant, and no further work can be done.

So, what is the flaw in the logic that suggests that pressurized gas has infinite potential energy? The answer lies in the fact that the potential energy of a system is always measured with respect to a reference point. In the case of expanding pressurized gas, the reference point is typically taken as the initial state of the gas. As the gas expands, its potential energy decreases, but it can never reach zero because that would require an infinite expansion. Therefore, the potential energy of the gas can never be infinite.

In conclusion, while the equation you were shown in your thermodynamics class may seem to suggest that pressurized gas has infinite potential energy, this is not the case. The equation is only applicable for finite expansions, and the potential energy of the gas is always measured with respect to a reference point. It is important to keep in mind the limitations and assumptions of any equation in order to fully understand its implications.