Question

A cylinder fitted with a piston has an initial volume of 0.1 m3 and contains nitrogen at 150 kPa, 25 0C. The piston is moved, compressing the nitrogen until the pressure is 1 MPa and the temperature is 150 0C. During this compression process heat is transferred from the nitrogen, and the work done on the nitrogen is 20 kJ. Determine the amount of this heat transfer.

Answer 1

A cylinder fitted with a piston has an initial volume of 0.1 m3 and contains nitrogen at 150 kPa, 25 0C. The piston is moved, compressing the nitrogen until the pressure is 1 MPa and the temperature is 150 0C. During this compression process heat is transferred from the nitrogen, and the work done on the nitrogen is 20 kJ. Determine the amount of this heat transfer.

Solution :-

Lets first calculate the mass of the nitrogen gas present using the ideal gas law formula

PV= mRT

R= 0.2968 kJ per kg K

T= 25 +273 = 298 K

V= 0.1 m3

P=150 kpa

m= (150 kpa * 0.1 m3 ) / (0.2968 kJ per kg K * 298 K)

m=0.1696 kg N2

now lets calculate the Delta E using the Cv of the N2 gas

Cv= 0.745 kJ per kg K

Delta E = Cv * delta T

T1 = 298 K

T2 = 150 C +273 = 423 K

Delta T= 423 – 298 = 125 K

Delta E = 0.745 kJ per kg K * 125 K

Delta E= 93.125 kJ

Delta E * m = Q-W

We have to find Q

Therefore Q = m*Delta E – w

                      = (0.1696 kg * 93.125 kJ per kg )- 20 kJ

                      = -4.206 kJ

Therefore amount of heat transferred = -4.206 kJ