Imagine that you have a gas confined in an insulated cylinder by a piston. Imagi

Question

Imagine that you have a gas confined in an insulated cylinder by a piston. Imagine that you suddenly push hard on the piston, compressing the gas to one-half its volume. Then you slowly let the gas expand back to its original volume. Will the gas have the same temperature as when you started? Will its entropy be the same as before? Would your answers be different if you had slowly compressed the gas and then slowly expanded it? Explain your responses carefully.

Hint: when you press the piston in suddenly, do you think that you exert more, less, or the same force on it that would if you were to compress the gas slowly?

Explanation / Answer

Given that the gas is confined in an insulated cylinder means no exchange of heat from inside to the surroundings or from surroundings to the inside. And also we can see that the expansion process is a very slow process. Indicating that the expansion is isothermal expansion. Hence the temperature remains constant. Secondly the process is a reversible process, as it reaches to its original position again. hence there will be no change in the internal energy and hence there will be no change in the entropy too. hence entropy of the system remains constant.

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