A massive piston traps a fixed amount of helium gas as shown. After being brough

Question

A massive piston traps a fixed amount of helium gas as shown. After being brought to point (a) the system equilibrates to room temperature. Weight is then added to the piston slowly so that the system remains at room temperature. Eventually, the gas is compressed to half of its original volume (b). The temperature Tb _________________ Ta. The internal energy Ub __________________ Ua. the pressure Pb _________________ Pa. The entropy of the gas at "b" is __________________ the entropy of the gas at "a". < than, > than, or equal to?

Explanation / Answer

Adiabatic, reversible = isentropic. Compressing the gas increases the pressure. The temperature should increase, but the system remains at room temp through the compression, so clearly heat must be leaving the system. So entropy must change. dS = dQ / T; T constant, dQ < 0 (heat leaves system to keep temp const), dS < 0 Temperature remains the same. Internal energy: dU = T dS - p dV dS < 0, p increases and dV < 0 : Just guessing at this one, but it should increase, because work is being done on the gas in excess of the heat being allowed to escape. i.e. T dS decreasing, but -p dV > 0 increasing faster than T dS decreasing. Pressure necessarily increases.

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