The change in the internal energy of the mass of gas, when the volume changes from V to 2 V at constant pressure P is ( = C _ P / C _ V )

Step-by-step solution

The change in internal energy for an ideal gas is given by U = n C_V T . For a constant pressure process where volume changes from V to 2V , the volume change is V = V . The work done by the gas is W = P V . From the ideal gas law PV = nRT , the temperature change relates to volume change at constant pressure as P V = nR T , yielding T = P V nR . Substituting into the internal energy expression gives U = C_V R P V . Using Mayer's relation C_P - C_V = R and the adiabatic index = C_P C_V , we obtain R = C_V( - 1) , s