Question

An ideal monatomic gas is adiabatically compressed so that its final temperature is twice its initial temperature. What is the ratio of the final pressure to its initial pressure?

Answer 1

Given : An ideal monatomic gas is adiabatically compressed so that its final temperature is twice its initial temperature.

To find : the ratio of the final pressure to its initial pressure.

solution : let initial temperature is T.

so the final temperature is 2T.

for ideal monoatomic gas, γ = 5/3

using formula, P^(1 - γ)T^γ = constant.

⇒P₁^(1 - γ)T₁^γ = P₂^(1 - γ)T₂^γ

⇒(P₁/P₂)^(1 - 5/3) = (T₂/T₁)^(5/3)

⇒(P₁/P₂)^(-2/3) = (2T/T)^(5/3)

⇒P₁/P₂ = (2)^{5/3 × -3/2 } = (2)^(-5/2)

⇒P₂/P₁ = (2)^(5/2) = 4√2

Therefore the ratio of final pressure to its initial pressure is 4√2 : 1.