CW03-04
\nExercise 4.1 Simple Changes in State
\nConsider one mole of an ideal gas with a molar heat capacity of Cv = 5R\/2. This gas is
\nexpanded from an inital state of T=300.0K and Volume of 10.0L to a final Volume of 20.0L
\nA. Consider a free expansion (pop = 0) of this gas between the endpoints defined above.
\ni What is the final pressure?
\nii What is Work?
\niii What is the change in Energy of the system, \u2206U?
\niv What is the change in Entropy of the system, \u2206S?
\nv What is the change in Entropy of the Universe, \u2206S Universe?
\nB. Consider the change in state of a single-stage isothermal expansion that creates the most usable
\n(most negative) Work between the endpoints defined above.
\ni What is the final pressure?
\nii What is Work?
\niii What is the change in Energy of the system, \u2206U?
\niv What is the change in Entropy of the system, \u2206S?
\nv What is the change in Entropy of the Universe, \u2206S Universe?
\nC. Consider the adiabatic (Q = 0) single-stage (constant external pressure) change in state that
\ncreates the most usable (most negative) Work between the endpoints defined above.
\ni What is the final pressure?
\nii What is Work?
\niii What is the change in Energy of the system, \u2206U?
\niv What is the change in Entropy of the system, \u2206S?
\nv What is the change in Entropy of the Universe, \u2206S Universe?
\nExercise 4.2 A Non-Ideal Gas
\nConsider a non-ideal gas that obeys the following equation of state:
\npV = RT + aT2
\nwhere a is a constant specific to the gas.
\nDerive an expression for the Work performed by this gas in a reversible isothermal expansion
\nfrom V1 to V2 at Temperature T
\n\u2014 CW03 continues \u2014
\nCHM4411 pjbrucat 2022 page 1
\nCW03-05
\nExercise 5.1 Isentropic Changes
\nMeteorologists often treat the bottom 10 km of the Earth\u2019s atmosphere as isentropic (having
\nconstant entropy). Assuming this to be true, and that the conditions at sea level are p = 1.000
\natm and T = 300.0 K, what should the temperature be at an altitude of 10.0 km where the
\npressure is 0.275 atm? Assume that air is an Ideal Gas with a constant volume heat capacity
\nof CV = 5R\/2
\nExercise 5.2 A Double Piston Apparatus Puzzle
\nA thermally insulated cylindrical container of fixed total volume is divided into three sections,
\nA, B, and C. Sections A and B are separated by a frictionless adiabatic piston (which transmits
\nwork but no heat), and sections B and C are separated by a frictionless diabatic (thermally
\nconductive) piston. Each section of the cylinder contains 1.000 mol of an ideal gas with
\nCV = 5R\/2. Initially, all three sections have a pressure of 1.000 atm and a temperature of
\n298.0 K. The gas is section A is heated (with an embedded resistive heater) slowly until the
\ntemperature in section C reaches 348.0 K.
\ni What is the final Temperature (in K) of the gas in section B?
\nii What is the final Volume (in L) in section B?
\niii What is the final Volume (in L) in section A?
\niv What is the final Temperature (in K) of the gas in section A?
\nExercise 5.3 Heat Capacity along a Path
\nThe heat capacity of an ideal gas is dependent on the path of the heating (or cooling) process.
\nA particular monoatomic (ideal) gas has a molar heat capacity of CV = 3R\/2 when heated
\n(or cooled) at constant volume. This same gas has a molar heat capacity of Cp = 5R\/2 when
\nheated at constant pressure.
\ni Why are the constant pressure and constant volume heat capacities different?
\nii What is the molar heat capacity of this same gas when it is heated (reversibly) at constant
\np\/V , i.e. what is Cp\/V ? (Constant p\/V means that the ratio of the pressure to the volume of
\nthe gas remains constant along the heating path)
\n\u2014 end of CW03 \u2014
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