**P. 4581.** A frictionlessly moveable piston of mass *m* confines *n*=0.25 moles of diatomic gas at a temperature of *T*_{1}=300 K in a vertical cylinder, closed at its bottom, of cross section *A*=2 dm^{2}. The piston is at a distance of *h*_{1}=3 dm from the bottom and the ambient pressure is *p*_{0}=10^{5} Pa.

The gas is heated in two steps. The first step lasts until the piston reaches the stoppers, in this stage the piston is *h*_{2}=5 dm from the bottom of the cylinder. The added heat in the second step, which begins when the piston reaches the stopper, is times as much as the added heat in the first step.

*a*) Determine the mass *m* of the piston.

*b*) What is the total force exerted by the stoppers on the piston at the end of the second heating step?

*c*) Plot the pressure of the gas as a function of the absolute temperature.

(5 points)

**Deadline expired on 10 December 2013.**

\(\displaystyle b)\) \(\displaystyle F=1{,}66~\)kN.