Answer to Question #169517 in Molecular Physics | Thermodynamics for Khushi

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

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

$V_2=0.5V_1,$

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

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

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

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