AxiomOfChoice
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Suppose you have a piston of ideal gas that's thermally isolated from its surroundings. You compress the gas by pushing down on the piston. Question: Does the temperature of the gas change, and why?
My answer: YES, it changes. Since \Delta U = Q + W, and work was done ON the gas (by compressing it), \Delta U > 0. Since the energy of an ideal gas is only dependent on the temperature of the gas, this implies \Delta T > 0.
My answer: YES, it changes. Since \Delta U = Q + W, and work was done ON the gas (by compressing it), \Delta U > 0. Since the energy of an ideal gas is only dependent on the temperature of the gas, this implies \Delta T > 0.