Question

Helium in a piston/cylinder at ${27}^{\circ }C,$ $100\text{kPa}$ is brought to $400\text{K}$ in a reversible polytropic process with exponent $n=1.25$. Helium can be assumed to be an ideal gas with constant specific heat capacity. Find the work done per unit mass of gas.
Assume $R$ for helium $=2.07\text{kJ/kg K}$

• A. $-587.7\text{kJ/kg}$
• B. $-687.7\text{kJ/kg}$
• C. $-787.7\text{kJ/kg}$
• D. $-828\text{kJ/kg}$

Answer 1

The correct option is D $-828\text{kJ/kg}$

We know that, work done during a polytropic process is given by
$W=\frac{P_2{V}_2-P_1{V}_1}{1-n}=\frac{R(T_2-T_1)}{1-n}$ [Where, mass $=1\text{kg}$]
From the data given in the question we get,
$W=\frac{2.07(400-300)}{1-1.25}=-828\text{kJ/kg}$
Thus, option (d) is the correct answer