question_answer 37)

                  Consider one mole of perfect gas in a cylinder of unit cross-section with a piston attached (fig.) 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 \[{{V}_{o}}\] to \[V\].                 (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 \[Q,\,{{P}_{a}},\,V\]. \[{{V}_{o}}\] and \[k\].

Answer:

                  (a) In equilibrium,                 Inside pressure = atmospheric pressure                 \[\therefore \]Initial pressure, \[{{P}_{i}}={{P}_{a}}\]                 (b) \[{{P}_{f}}={{P}_{a}}+k(V-{{V}_{0}})\]