Homework 6 Home Page

Problem 6.3 Hint

Use the result of Pblm. 5.4 to get results into natural cooridinates

Extra Problem

A vertical cylinder contains v moles of an ideal gas and is closed off by a piston of mass M and area A. The acceleration due to gravity is g. The molar specific heat c_v (at constant volume) of the gas is a constant independent of temperature. The heat capacities of the piston and cylinder are negligibly small and any frictional forces between the piston and the cylinder walls can be neglected. The whole system is thermally insulated. Initially, the piston is clamped in position so that the gas has a volume V_o and a temperature T_o. The piston is now released and, after some oscillations, comes to rest in a final equilibrium situation corresponding to a larger volume of the gas.

  1. Does the temperature of the gas increase, decrease, or remain the same?
  2. Does the entropy of the gas increase, decrease, or remain the same?
  3. Calculate the final temperature of the gas in terms of T_o, V_o, and the other parameters mentioned in the statement of the problem.
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