Question

Consider one mole of perfect gas in a cylinder of unit cross section with a piston attached (Fig. 12.12). A spring (spring constant k) is attached (unstretched length L ) to the piston and to the bottom of the cylinder. Initially the spring is unstretched and the gas is in equilibrium. A certain amount of heat Q is supplied to the gas causing an increase of volume from V0 to V1.

(a) What is the initial pressure of the system?

(b) What is the final pressure of the system?

(c) Using the first law of thermodynamics, write down a relation between Q, Pa, V, Vo and k.

Answer 1

(a) Pi = Pa

(b) Pf = Pa + k/A ( V - Vo ) = Pa + k(V - Vo)

(c) All the supplied heat is converted to mechanical energy. No change in internal energy (Perfect gas)