A gas at pressure p is adiabatically compressed so that its density becomes twice that of initial value…

Q: A gas at pressure p is adiabatically compressed so that its density becomes twice that of initial value. Given that γ = Cp/Cv = 7/5 , What will be the final pressure of the gas ?

(a) 2 p

(b) 7/5 p

(c) 2.63 p

(d) p

Ans:(c)

Sol: As , $\displaystyle P_2 V_2^\gamma = P_1 V_1^\gamma $

$ \displaystyle P_2 = P_1 (\frac{V_1}{V_2})^\gamma $

$ \displaystyle P_2 = P_1 (\frac{\rho_2}{\rho_1})^\gamma $

$ \displaystyle P_2 = P_1 (\frac{2 \rho_1}{\rho_1})^\gamma $

$ \displaystyle P_2 = p (\frac{2}{1})^{7/5} $

P2 = 2.63 p