Sketch of piston-spring systems
The figure shows three identical chambers containing a piston and a spring with spring constant k. The chamber in a is completely evacuated, and the piston just touches its left end. In this position, the spring is relaxed. In b, the chamber contains n mol of ideal gas 1 in the space to the left of the piston, and the spring is compressed with an amount X-----1. Inc, the chamber contains n mol of ideal gas 2 and the spring is compressed with an amount X-----2.
1) Which gas exerts the greater force on the piston? Ideal gas 1 or ideal gas 2?
2) Which gas exerts the greater pressure on the piston? Ideal gas 1 or ideal gas 2?
3) Which gas has the larger temperature? Ideal gas 1 or ideal gas 2? Give a brief description.
4) Utilize the ideal gas law to find an expression for the temperature in terms of the spring constant k, the displacement X, the number of moles n, and the ideal gas constant R
Hint: Express the volume of the gas in terms of the displacement X and the area A of the piston; express the pressure of the gas in terms of the spring constant k, the displacement X and the area A of the piston.