The correct option is C 4P
Initially, ideal gas undergoes isothermal expansion.
For an isothermal process, temperature remains constant
i.e P1V1=P2V2
From the data given in the question,
PV=16V×P′
P′=P16 ......(1)
Later, gas undergoes adibatic compression to come back to initial volume V.
Let the final pressure be P′′.
The equation of state in terms of P and V is given by
P2Vγ2=P′′Vγ1
From the data given in the question, we get
P′×(16V)1.5=P′′×(V)1.5 (∵P2=P′ and V2=16V)
P16×(16V)1.5=P′′×(V)1.5
⇒P′′=4P
Thus, option (c) is the correct answer.