A gas is enclosed in a cylindrical can fitted with a piston. The walls of the can and the piston are adiabatic. The initial pressure, volume and temperature of the gas are 100 kPa, 400 cm^{3} and 300 K respectively. The ratio of the specific heat capacities of the gas is C_{P}/C_{V} = 1.5. Find the pressure and the temperature of the gas if it is

(a) suddenly compressed

(b) slowly compressed to 100 cm^{3}.

Given, P1 = 100 KPa = 10^{5} Pa, V1 = 400 cm^{3} , T1 = 300 K,

C_{P}/C_{V} = 1.5

(a)Suddenly compressed to V2 = 100 cm^{3} I.e. it is an adiabatic process

∴ PV^{γ} = const.

I.e.

Also,

(b) Even though the container is slowly compressed the walls are adiabatic so heat transferred is 0.

Thus the values remain same

i.e. P2 = 800 KPa, T2 = 600 K.

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