In isothermal expansion, p1V1=p2V2 ⇒p0V1=p2.8V1[∵V2=8V1] ⇒˙p2=p0/8 Now; gas is slowly and adiabatically compressed back to its initial volume. Hence, for this adiabatic compression, p1=p0∕8,V1=8V p2=?,V22=V ∴ Using adiabatic relation, p1V1γ=p2V2γ
⇒
p0
8
⋅(8V)γ=p2(V)γ⇒
p0
8
⋅8γ⋅Vγ=p2V′
⇒
p0
8
⋅8γ=p2⇒p2=
p0
8
⋅8γ =
p0
8
⋅(8)
4
3
[∵γ=
4
3
] =
p0
8
⋅16 ⇒p2=2p0 ∴ Average kinetic energy per molecule, K=