Question

When a certain perfect gas is heated at constant pressure from 15 oC to 95 oC, the
heat required is 1136 kJ. While when the same gas is heated at constant volume
between the same temperature limit above the heat required is 808 kJ. Calculate
cp,cv,

, R and molecular weight of the gas.

Answer 1

$T_1=15°$

$T_2=95°$

$\Delta Q_1=1136\frac{kJ}{kg}$

$\Delta Q_2=808\frac{kJ}{kg}$

$\Delta Q_1=c_p\Delta T \to c_p=\frac{\Delta Q_1}{\Delta T}=\frac{1136000}{80}=14200\frac{J}{kg\cdot K}$

$\Delta Q_2=c_V\Delta T \to c_V=\frac{\Delta Q_2}{\Delta T}=\frac{808000}{80}=10100\frac{J}{kg\cdot K}$

$\gamma=\frac{c_p}{c_V} =\frac{14200}{10100}=1.4$

$R_m=c_p-c_V=14200-10100=4100\frac{J}{kg\cdot K}$

$R=R_m\cdot M\to M=\frac{R}{R_m}=\frac{8.31}{4100}=0.002 \frac{kg}{mol}$

The gas is hydrogen ($H_2$ ).