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The initial pressure and volume of a given mass of a gas (CP/CV = γ) are P0 and V0. The gas can exchange heat with the surrounding.
(a) It is slowly compressed to a volume V0/2 and then suddenly compressed to V0/4. Find the final pressure.
(b) If the gas is suddenly compressed form the volume V0 to V0/2 and then slowly compressed to V0/4, what will be the final pressure?
Given CP/CV = γ
Let P1=P0 be the Initial Pressure, V1=V0 be the Initial Volume
(a)Since the volume is slowly compressed, temperature remains constant I.e. Isothermal compression. Let P2 and V2=V0/2 be the pressure and volume after slow compression
∴
When volume is suddenly compressed, it is an adiabatic process .Let P3 and V3 be the pressure and volume after sudden compression .i.e.
PVγ = const.
I.e.
Substituting value of P2=2P0
(b) Since the volume is suddenly compressed, I.e. it is an adiabatic process Let P2 and V2=V0/2 be the pressure and volume after sudden compression, then
PVγ = const.
I.e.
Substituting value of P1=P0
Now, since the volume is slowly compressed, temperature remains constant I.e. Isothermal compression. Let P3 and V3=V0/4 be the pressure and volume after slow compression.
∴