# 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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