UNIFIED ENGINEERING Fall 2006

Ian A. Waitz

Problem T4 (Unified Thermodynamics)

Below is a piston-cylinder arrangement where the piston has two chambers. Although the cylinder is thermally-insulated from the surroundings, the lower chamber is isolated by a thin copper barrier, which is rigid but which allows the slow transfer of heat between the two chambers. The cylinder walls are rigid. The chambers are filled with air which behaves as an ideal gas with R=287 J/kg-K and you can assume the specific heats are constant at c_v=716.5 J/kg-K, c_p=1003.5 J/kg-K.

Both chambers start in thermodynamic equilibrium with T=300K, p=100x10³ Pa with a volume of 0.1 m³. A weight equivalent to an external pressure of 1000x10³ Pa is instantaneously dropped on the upper cylinder. You can assume that the piston itself is massless and free to move without friction. Your objective is to devise a simplified thermodynamic model of this system and to use it to estimate the temperature the gas in the lower chamber would come to when the two-chamber system eventually comes to thermodynamic equilibrium.

a)     Describe the energy exchange processes in the device in terms of heat, work and various forms of energy. (LO’s #1, #2)

b)    What processes will you use to model this system?  Why?  (LO’s #2, #4, #5)

c)     What is the temperature the gas in the upper chamber comes to shortly after the instantaneous dropping of the weight? (LO #4)

d)    What is the temperature the gas in the lower chamber comes to when the whole system eventually reaches thermodynamic equilibrium? (LO #4)