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 cm3 and 300 K respectively. The ratio of the specific heat capacities of the gas is CP/CV = 1.5. Find the pressure and the temperature of the gas if it is
(a) suddenly compressed
(b) slowly compressed to 100 cm3.
Given, P1 = 100 KPa = 105 Pa, V1 = 400 cm3 , T1 = 300 K,
CP/CV = 1.5
(a)Suddenly compressed to V2 = 100 cm3 I.e. it is an adiabatic process
∴ PVγ = 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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