Question

Calculate the internal energy and the enthalpy of 1 kg of air occupying 0.05 m3
at
20 oC at 20 bar. If the internal energy is increased by 120 kJ as the air compressed
to 50 bar. Calculate the new volume occupied by 1 kg of air.

Answer 1

We will assume that gas is ideal. So, the internal energy of air

$U=\frac{m}{M}C_VT$

For air $M=28.96 \cdot 10^{-3}kg/mol$ and $C_V=\frac{i}{2}R=\frac{5}{2}\cdot 8.31\approx20.8\frac {J}{mol\cdot K}$

$U=\frac{m}{M}C_VT=\frac{1}{28.96 \cdot 10^{-3}}\cdot 20.8\cdot 293=210442J$

The enthalpy of air

$H=U+pV=210442+2\cdot 10^6\cdot 0.05=310442J$

$\Delta U=\frac{m}{M}C_V(T_2-T_1)\to T_2=\frac{\Delta U\cdot M}{m\cdot C_V}+T_1=$

$=\frac{120000\cdot 28.96\cdot 10^{-3}}{1\cdot 20.8}+293=460 K$

$\frac{p_1V_1}{T_1}=\frac{p_2V_2}{T_2}\to V_2=\frac{p_1V_1T_2}{T_1p_2}=$

$V_2=\frac{p_1V_1T_2}{T_1p_2}=\frac{2\cdot 10^6\cdot 0.05\cdot 460}{293\cdot 5\cdot10^6}=0.031m^3$