Piston displacement

The device consists of a piston and cylinder with air of mass \(m\) contained within it. The cylinder and piston are perfectly insulated, therefore there is no heat transfer between system and surroundings.

A Block weighing \(W=1000 \text{ N}\) is placed on the piston and the system is allowed to come to equilibrium. Now \(Q=1 \text{ KJ}\) amount of heat is added to the system due to which the piston moves up by a distance \(h\) but this happens very slowly (Quasi-equilibrium process).

Case 1: The device is kept in vacuum. \({ P }_{ \text{atm} }=0 \text{ KPa}\)
Let the distance moved by the piston in this case be \({ h }_{ 1 }\).

Case 2: The device is kept in a place where \({ P }_{\text{atm} }=100 \text{ KPa}\) Let the distance moved by the piston in this case be \({ h }_{ 2 }\).

Evaluate \( { h }_{ 1 }-{ h }_{ 2 } \) in \(\text{cm} \).

Details and Assumptions:

  1. Area of the piston = \(150 \text{ cm }^{ 2 }\).
  2. Heat capacity ratio of air \(\gamma \) = \(\frac { { c }_{ p } }{ { c }_{ v } } =1.4\), \({ c }_{ p }\) and \({ c }_{ v }\) indicates specific heat at constant pressure and volume respectively.
  3. Piston weight is negligible.
  4. Air can be treated as an ideal gas.
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