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A gas in a well-insulated cylinder pushes a piston out against a steady outside pressure of 0.90 ×…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A gas in a well-insulated cylinder pushes a piston out against a steady outside pressure of , from to litres. Find the work done by the gas and the change in its internal energy. Does it get warmer or cooler?
Need a reminder? The key ideaShow
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.
Work done by a gas is the area under its path on a pressure-volume graph. At a steady pressure ; along a straight line, the average pressure times ; at a steady temperature . Expanding gives positive work, squeezing negative. .
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. .
Step 2. First law. , so .
Answer: of work; the internal energy falls by , so the gas cools.
Watch out. Use the outside pressure the gas pushes against, not its own changing pressure.
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