Question

An ideal gas at pressure p is adiabatically compressed so that its density becomes n times the initial value. The final pressure of the gas will be

Answer 1

Answer:

an ideal gas at pressure P is adiabatically compressed so that its density becomes n times the initial value. if ɤ=CP/CV.

THEN WHAT WILL BE THE FINAL PRESSURE

Answer 2

Answer:

$P_2=n^{\gamma} P$

Explanation:

Given that

Initial pressure (P₁)=P

Initial density =ρ

Final density = nρ

For adiabatic compression

$PV^{\gamma}=C$

P=pressure

V=volume

γ=Heat capacity ratio

We also know that ideal gas

P = ρ RT

$P\rho^{-\gamma}=C$

Lets final pressure = P₂

$P_1\rho^{-\gamma}=P_2(n\rho)^{-\gamma}$

$P\rho^{-\gamma}=P_2(n\rho)^{-\gamma}$

$P_2=n^{\gamma} P$

This is final pressure.