  Question

# The initial pressure & volume of a given mass of gas (CPCV=53) are P0 and V0. The gas can exchange heat with the surroundings. It is slowly compressed to volume V04 and then suddenly compressed to volume V08 and then again slowly compressed to V016. Find the final pressure.

A
2143P0
B
2113P0
C
273P0
D
253P0

Solution

## The correct option is A 2143P0We know that, when a gas is compressed slowly, the process is isothermic and when it's quickly compressed, process is adiabatic. Step I (isothermal compression) : We know that equation of state for an isothermal process is given by, P1V1=P2V2 From the data given in the question, P0×V0=P′×V04 ⇒P′=4P0 ......(1) Step II (adiabatic compression) : From the equation of state for an adibatic process in terms of P and V, we can write that P2Vγ2=P3Vγ3 From the data given in the question, P′×(V04)53=P′′×(V08)53 Using (1), P′′=4P0×(2)53 ......(2) ⇒P′′=P0×253+2=2113P0 atm Step III (isothermal compression) : We can write from the data given in the question that,  P′′V08=P′′′V016 ⇒P′′′=2×2113P0 ⇒P′′′=2143P0 Thus, option (a) is the correct answer.  Suggest corrections   