1. [40 points] An insulated piston and cylinder assembly contains a...

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1. [40 points] An insulated piston and cylinder assembly contains an ideal gas with a heat capacity at constant volume equal to 1.5 R (R is gas constant). The piston, which is backed by a vacuum, initially is held in place by the lower of the two mechanical stops. When the local mechanical stop is released, the piston rises until it encounters a second mechanical stop. The volume after the expansion is 50% larger than the original volume, and the temperature drops to 75% of its initial value. a. Determine the mass of the piston in terms of the gas constant, R, the acceleration due to gravity, g and the vertical displacement of the piston between the two mechanical stops, z. b. Determine the total entropy change of the universe in terms of R for this process. Is this process reversible or irreversible? 2. [30 points] A gas at high pressure flows through a duct and a thermometer in the duct reads 200 K. A small amount of gas is bled out of this duct through an insulated throttle valve open to the atmosphere. The temperature of the gas leaving the throttle is measured at 180 K. What is the pressure of the gas in the high-pressure duct? The gas obeys the equation of state: 𝑃𝜈 𝑅𝑇 = 1 + (𝑏 − 𝑎 𝑇 ) 𝑃 𝑅𝑇 where b = -20 cc/mol and a = 40000 cc-K/mol. The molar heat capacity of the gas at low pressure is Cp = 10+0.02 T (T is in K, cal/mol-K).

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