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0.75 mol of an ideal gas in an insulated box rushes into a vacuum when a wall is removed, growing…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
of an ideal gas in an insulated box rushes into a vacuum when a wall is removed, growing to times its volume. Find , and for the gas, and its change of entropy. How can the entropy change with no heat? ()
Need a reminder? The key ideaShow
Heat taken in slowly at a steady temperature raises the entropy by . Warming from to : . A gas at a steady temperature: . Entropy depends only on the state, and the total for an isolated system never falls.
The first law: . is positive when heat goes into the gas; is positive when the gas does work on its surroundings, so work done on the gas is negative. For an ideal gas, means it gets warmer.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. Work, heat and energy. Nothing to push against: . Insulated: . So , and the temperature does not change.
Step 2. Entropy. Along a slow isothermal path between the same two states, .
Answer: ; .
Watch out. only holds along a reversible path. A free expansion is irreversible, so its entropy rises with no heat at all.
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