The tank below has a frictionless, adiabatic (no heat conduction) piston that se

Question

The tank below has a frictionless, adiabatic (no heat conduction) piston that separates an ideal gas on the left from water on the right. The initial pressure and volume of the ideal gas is 50 kPa and 8 liters. The initial pressure and temperature of the water is 50 kPa and 25C. Heat is added slowly to the water until the volume of the ideal gas is 1 liter. During the compression of the ideal gas heat transfer maintains the ideal gas at constant temperature (initial temperature). If the mass of the water is 5 kg, determine the necessary heat transfer. There are various pieces of knowledge you have to bring together to solve this problem. First you must picture what is happening physically. P is not constant.

Explanation / Answer

Since Temperature is constant

P1*V1 = P2*V2

P2 = 50*8/1 = 400 kPa

Work done in isothermal process

W = -P1*V1*ln(P1/P2) = -50*8*ln(50/400) = 831.78 J

Since the temperature is constant

change in internal enegy(dU) = 0

dQ = dU + W

dQ = W = 831.78 J

The heat added to the water must be 831.78 kJ

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