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

Answer:

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

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:

$W=RT_{1}ln\frac{P_{1}}{P_{2}}$

$W=0.287(77+273)ln\frac{7.6}{3.05}$

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:

$W=RT_{1}ln\frac{P_{1}}{P_{2}}$

$W=4.1242(77+273)ln\frac{7.6}{3.05}$

W = 1317.89 kj/kg.

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