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                                    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 temperture of the gas are `100 kpa, 400cm^(3)` and `300k` 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). | 
                            
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Answer» `P_1=100 Kpa` , `V_1 = 400 cm^3`, `=400xx10^(-6)m^3`, `T_1=300K`, `gamma=(Cp)/(Cv) = 1.5` (a) Suddenly compressed to `V_2 = 100 cm^3` `P_1V_1^gamma = P_2V_2^gamma` implies 10^5 xx (400)^1.5 = P_2(100)^1.5` `P_2 = 10^(5)(4)^1.5 = 800 KPa` `T_1V^(gamma-1)=T_2V_2^(gamma-1)` implies `300xx(400)^(1.5-1) = T_2(100)^(1.5-1)` implies `300 xx (400)^0.5 = T_2 (100)^0.5` `T_2 =600K`. (b) Even if the container is slowly compressed the walls are adiabatic so heat transferred is zero. Thus the values remain, `P_2=800 KPa` `T_2 =600 K`  | 
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