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assignment 7

# assignment 7 - Thermal Physics PHYS‐253 Assignment 7 due...

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Unformatted text preview: Thermal Physics PHYS‐253 Assignment 7, due 12 November (2010) in class 1) Prove that the slope on a TS diagram of a) An isochoric curve is T/CV b) An isobaric curve is T/Cp 2) a) One kilogram of water at 273K is brought into contact with a heat reservoir at 373K. When the water reached 373K, what is the entropy change of the water, of the heat reservoir and the universe? b) If the water had been heated from 273K to 373K by first bringing it into contact with a reservoir at 323K and then with a reservoir at 373K, what would have been the entropy change of the universe? c) Explain how the water might be heated from 273K to 373K with almost no change of entropy of the universe. 3) A thermally insulated cylinder, closed on both ends, is fitted with a frictionless heat‐conducting piston that divides the cylinder in two parts. Initially, the piston is clamped in the center with 1 liter of air at 300K and 2 atm pressure on one side and 1 liter of air at 300K and 1 atm pressure on the other side. The piston is released and reaches equilibrium in pressure and temperature at a new position. Compute the final pressure and temperature and increase of entropy if air is assumed to be an ideal gas. What irreversible process has taken place? 4) An adiabatic cylinder, closed at both ends, is fitted with a frictionless adiabatic piston that divides the cylinder into two parts. Initially the pressure, volume, and temperature are the same on both sides of the piston (p0, V0, and T0). The gas is ideal with CV independent of temperature and =1.5 . By means of a heating coil in the gas on the left side, heat is slowly supplied to the gas on the left until the pressure reaches 27p0/8. In terms of nR, V0 and T0: a) What is the final volume on the right side? b) What is the final temperature on the right side? c) What is the final temperature on the left side? d) How much heat must be supplied to the gas on the left side? (note: ignore the coil) e) How much work is done on the gas on the right side? f) What is the entropy change of the gas on the right side? g) What is the entropy change of the gas on the left side? h) What is the entropy change of the universe? ...
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