For an ideal gas, the internal energy is given by U = 5   p V / 2 + C , where C is a constant. The equation of the adiabats in the p V -plane will be

Step-by-step solution

For an ideal gas, C V = ∂ U ∂ T V = constant or C V = d U d T Also, for 1 mole of gas, C V = f 2 · R where, f = degree of freedom. Hence, we have f 2 R = d U d T Here, U = 5 2 p V + C = 5 2 R T + C [ ∵ one mole of gas is considered] So, f 2 R = d d T 5 2 R T + C ⇒ f 2 R = 5 2 R ⇒ f = 5 Now, using γ = 1 + 2 f where, γ = ratio of specific heats = adiabatic index. We have, γ = 1 + 2 5 ⇒ γ = 7 5 So, equation of adiabats can be written as p V γ = constant