One mole of an ideal gas is taken from an initial temperature T₀ to a final temperature 2T₀ along a process defined by the relation PT^2 = constant , where P is the pressure and T is the absolute temperature. The work done by the gas during this process is :

Step-by-step solution

The given process equation is PT^2 = constant . From the ideal gas equation for one mole, T = PV R . Substituting this into the process equation gives: P ( PV R )^2 = constant P^3V^2 = constant ' Taking the cube root of both sides, we get the standard polytropic form PV^x = constant : PV^ 2/3 = constant '' Thus, the polytropic exponent is x = 2 3 . The work done in a polytropic process in terms of temperature is given by: W = nR(T₁ - T₂) x-1 Substituting n = 1 , T₁ = T₀ , T₂ = 2T₀ , and x = 2 3 : W = R(T₀ - 2T₀) 2