3 kg of Hydrogen gas at P 1 bar and T 20 degree C is adiab

3 kg of Hydrogen gas at P = 1 bar and T = 20 degree C is adiabatically compressed to a pressure of 20 bar. Find the volume of the gas after compression.

Solution

in adiabatic process

PV^(gamma) = constant

gamaa = 1 + 2/f = 1+ 2/3 = 5/3 for hydrogen

=> P1V1^5/3 = P2V2^5/3

=> 1*V1^5/3 = 20*V2^5/3

=> V2 = (1/20)^3/5*V1

P1V1 = nRT1

=> 3 kg into moles = 3*1000/2 = 1500 moles

=> 100000*V1 = 1500*8.314*(273+20) ( 1 bar = 100000 Pa)

=> V1 = 36.54 m^3

=> V2 = 36.54*(1/20)^3/5 = 0.0009135 m^3