Question

A mass of 0.25 kg of an ideal gas at pressure 300 kPa, temperature ${80}^{o}C$ and a volume of 0.07 m${}^3$. The gas undergoes an irreversible adiabatic process to a final pressure of 300 kPa, and final volume 0.1 m${}^3$, during which work done on the gas is 25 kJ. The value of $c_v$, is ______ kJ/ kgK.

• A. $0.55\text{kJ/kgK}$
• B. $0.661\text{kJ/kgK}$
• C. $0.861\text{kJ/kgK}$
• D. $0\text{kJ/kgK}$

Answer 1

The correct option is B $0.661\text{kJ/kgK}$

$P_1=300kPa$, $P_2=300kPa$

$T_l=353K$, $V_2=0.1m^3$

$v_1=0.07m^3$, $W_{1-2}=-25kJ$

$m=0.25kg$
(- ve sign since work done on the gas)

​​​​​​$\Rightarrow$ $T_2=\frac{P_2{V}_2}{P_1{V}_1}\times T_1$

$\Rightarrow$ $T_2=\frac{300\times 0.1}{300\times 0.07}\times 353$

$\Rightarrow$ $T_2=504.29K$

Now, $Q=\Delta U+W$

Since adiabatic process $Q=0$

$\Rightarrow$ $\Delta U=-W$

$\Rightarrow$ $C_v[T_2-T_1]m=-[-25]$

$\Rightarrow C_v=\frac{25}{(504.29-353)\times 0.25}=0.661kJ/kgK$