Question

Air in an enclosure is compressed isothermally until its pressure is doubled. It is

then expanded adiabatically until its original volume is restored. Its pressure is

then recorded as 0.75 of its initial value. Determine the value of gama.

Answer 1

$p_1V_1=p_2V_2,~ p_2=2p_1,\implies$

$V_2=0.5V_1,$

$p_2V_2^{\gamma}=p_3V_3^{\gamma},$

$p_3=0.75p_1,~ V_3=V_1,$

$2\cdot 0.5^{\gamma}=0.75,$

$\gamma=3-\text{log}_2 3\approx1.415.$