Question

Air at a pressure of 100 kPa has a volume of 0.32 m³. The air is compressed in a reversible adiabatic manner until the temperature is 190 ^oC. The reversible work is -63 kJ/kg. Determine the initial temperature.

t =

Answer 1

For air $k=1.4,$

$A=\frac{p_1V_1}{k-1}(1-(\frac{V_1}{V_2})^{k-1}),\implies$ $V_2=\frac{V_1}{1-(\frac{(k-1)A}{p_1V_1})^\frac 1{k-1}},$

$T_1V_1^{k-1}=T_2V_2^{k-1},\implies$

$T_1=\frac{T_2}{1-(\frac{(k-1)A}{p_1V_1})^\frac 1{k-1}}=208~K,$ or

$t_1=-65°C.$