An ideal gas having pressure P , volume V and temperature T is expanded isothermally, to a volume 3V and final pressure P_I . The same gas is expanded adiabatically to a volume 3V , the final pressure being P_A . The ratio P_A P_I is ( C_P C_V = )

Step-by-step solution

For the isothermal expansion, the temperature remains constant. Using Boyle's law: P₁ V₁ = P₂ V₂ P V = P_I (3V) P_I = P 3 For the adiabatic expansion, the relation between pressure and volume is: P₁ V₁^ = P₂ V₂^ P V^ = P_A (3V)^ P_A = P 3^ Taking the ratio of the final pressures: P_A P_I = P 3^ P 3 = 3 3^ = 3^ 1- Answer: 3^ (1- )