## Book: HC Verma - Concepts of Physics Part 2

### Chapter: 27. Specific Heat Capacities of Gases

#### Subject: Physics - Class 12th

##### Q. No. 20 of Exercises

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20
##### 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.

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