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Today in an engineering thermodynamics lecture, the professor gave an example of a gas doing work. We had a cylinder full of helium at a pressure of something like 200 kPa absolute and the valve was opened so that the gas would flow out against the atmospheric pressure until the pressures were equal. Also the cylinder was assumed to be in thermal equilibrium with its surroundings so the temperature of the gas was equal to the temperature of the ambient air. However, the way he calculated the work perturbed me. He said that this was an isobaric process because the gas was expanding against a constant atmospheric pressure. I was under the assumption that an isobaric process means that the working fluid stays at constant pressure throughout the process which is not the case in this expansion. And in this case, the gas pressure is dropping as it leaves the cylinder.

The professor then proceeded to calculate the work as $W = P_\text{atm}\Delta V$. But I didn't think that was right and that simple.

I should also note that the system was modeled as a closed system, so the gas inside the cylinder and the escaping gas were the system.

If this is not an isobaric process why is the work calculated with a constant pressure?

Am I correct, or is the professor?

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  • $\begingroup$ What is doing work on what here? What volume is changing? As I was reading I expected some type of movable piston. I must be missing something. $\endgroup$ – BMS Jan 28 '14 at 2:09
  • $\begingroup$ The pressurized gas is doing work on the atmosphere, from what I understand $\endgroup$ – user38397 Jan 28 '14 at 2:22
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I feel I could make sense of this if I first consider the system of only the atmosphere. In that case, one assumes the atmosphere is at constant pressure $P_\text{atm}$. The change in volume $\Delta V$ of the atmosphere could be calculated by knowing the initial and final states of the gas in the cylinder, and first calculating the amount ($N$) of gas entering the atmosphere. One could then calculate work by $W=P_\text{atm}\Delta V$.

Not sure if this result could apply to the system of gas originally enclosed in the cylinder. Someone better than me might chime in.

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  • $\begingroup$ The prof stated that the system just consisted of the pressurized gas only, and drew the system so that some of the boundary was around the gas in the cylinder and around the gas that was escaping out of the cylinder too. Eventually most of the gas would be out of the cylinder and for convenience sake stays together (forget entropy here!). $\endgroup$ – user38397 Jan 28 '14 at 2:48
  • $\begingroup$ Modified last paragraph to address my misreading. $\endgroup$ – BMS Jan 28 '14 at 3:04
  • $\begingroup$ Thanks for your take BMS, I think I agree with you on looking at the atmosphere as the system. $\endgroup$ – user38397 Jan 28 '14 at 3:57
  • $\begingroup$ This question confuses me very much, if he's talking about an isobaric system at 1 atmosphere pressure, where the gas remains in thermal equilibrium inside and outside of the bottle - the valve must be closed, or at the very least tending towards the infinitesimally open? I can't make sense of it otherwise. $\endgroup$ – Bitter dreggs. Jan 28 '14 at 20:01

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