For the isothermal expansion of a gas into a vacuum, ΔE = 0, q = ...

Question

For the isothermal expansion of a gas into a vacuum, ΔE = 0, q = 0, and w = 0. (b) Explain why no work is done by the system during this process.

Accepted Answer

Hello everyone. So in this video we're given several statements and we're trying to see which one is the correct explanation for why the system does not perform any work in this process. So, in the different statements, we see that we're dealing with ideal gas and this vessel. So the first thing to do is go ahead and to identify the components which which we just did. Now we have to match their roles. So whenever we're dealing with work, we have to identify the system, the surroundings and anything else that these statements do mention in our case for our ideal gas, that's going to be our system. So that's going to be what we're primarily focusing on for our surroundings. It's going to be everything else. As for our vessel, what that tells us is that there's going to be no other gas molecules inside the vessel. So, since there's nothing inside the vacuum, there's going to be no external factor affecting the system. In a case, like we said, our system is the ideal gas. So there's nothing that will affect the ideal gas and therefore no work is being done as this continues to expand. So the equation that we have for work is that work equals to the negative pressure. Alright, external pressure multiplied by our delta V and V. In our cases, of course, volume. And we're being told that the external pressure is equal to zero and the work is equal to zero. So if we plug those zeroes in, you can see that it's just everything will be zero. So then we can conclude that the correct answer and the correct statement is statement D. That reads the ideal gasses inside a vessel containing the vacuum where there is no other external pressure acting on it. Therefore, no work is done. So D is going to be my final answer for this problem.

For the isothermal expansion of a gas into a vacuum, ΔE = 0, q = 0, and w = 0. (b) Explain why no work is done by the system during this process.

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