A monatomic gas at pressure P1, and volume V1, iscompressed adiabatica

1.	A monatomic gas at pressure P1, and volume V1, iscompressed adiabatically to (1/8) th its original volumeWhat is the final presssure of the gas?(1) 64 P1(2) P1(3) 16 P1(4) 32 P1
Answer» The correct answer is option (4) - 32 P1 Solution: Let’s assume the initial pressure to be P, final pressure to be P2 and initial volume to be V. It is given that for a monoatomic gas γ = 5/3 For adiabatic process PV^γ = constant PV^5/3=P (V/8)^5/3 P2 =P(8)^5/3 P2 = P ×2⁵ Therefore, P2 = 32P

A monatomic gas at pressure P1, and volume V1, iscompressed adiabatically to (1/8) th its original volumeWhat is the final presssure of the gas?(1) 64 P1(2) P1(3) 16 P1(4) 32 P1

Answer»

The correct answer is option (4) - 32 P1

Solution:

Let’s assume the initial pressure to be P, final pressure to be P2 and initial volume to be V.

It is given that for a monoatomic gas γ = 5/3

For adiabatic process PV^γ = constant

PV^5/3=P (V/8)^5/3

P2 =P(8)^5/3

P2 = P ×2⁵

Therefore, P2 = 32P