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:
𝑅𝑇 = 1 + (𝑏 −
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).
These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction
of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice.
Unethical use is strictly forbidden.