Question

A gas is compressed isothermally in a piston-cylinder assembly from 7.6 bar, 77 °C to 3.05 bar. Determine the work and heat transfer, kJ/kg, for the following gases. a) Air b) Hydrogen

Answer 1

The work done or the heat transfer for air and hydrogen are 91.71 kj/kg and 1317.89 kj/kg respectively.

Step-by-step explanation:

Given:

Initial pressure is 7.6 bar.

Initial temperature is 77 °C.

Final pressure is 3.05 bar.

Calculation:

(a)

Take air as an ideal gas with gas constant 0.287 kj/kgK.

Step1

For isothermal process work done and heat transfer is the same because of no change in internal energy.

Work done is calculated as follows:

`W=RT_(1)ln(P_(1))/(P_(2))`

`W=0.287(77+273)ln(7.6)/(3.05)`

W = 91.71 kj/kg.

Thus, the work done or the heat transfer for isothermal process is 91.71 kj/kg.

Step2

For isothermal process work done and heat transfer is the same because of no change in internal energy. Take Hydrogen as an ideal gas with gas constant 4.1242 kj/kgK.

Work done is calculated as follows:

`W=RT_(1)ln(P_(1))/(P_(2))`

`W=4.1242(77+273)ln(7.6)/(3.05)`

W = 1317.89 kj/kg.

Thus, the work done or the heat transfer for isothermal process is 1317.89 kj/kg.