Three moles of a gas at a temperature ' T ' is heated to thrice its volume by keeping the pressure constant. If ' is the ratio of specific heats, then the increase in internal energy of the gas is

Step-by-step solution

Number of moles, n =3 Initial volume, V _ i = V Final volume, V _ f =3 ~V Ratio of specific heat, = C_p C_v Change in internal energy, V = nfR T 2 Degree of freedom; f = 2 -1 At constant pressure, V ₁ ~T ₁ = V ₂ ~T ₂ V T = 3 ~V ~T ₂ T ₂=3 ~T Substitute T ₂ in equation (1) aligned V & = nfR 2 ( ~T ₂- T ₁ ) = 3 2 & 2 R -1 (3 ~T - T ) & 3 R 2 ~T -1 U & = 6 RT -1 aligned