n moles of an ideal gas expand adiabatically such that its pressure is proportional to T^ 5/2 , where T is the absolute temperature. If the expansion causes the temperature of the gas to decrease by T , the work done by the gas is :

Step-by-step solution

For an adiabatic process, the relation between pressure P and temperature T is derived from PV^ = constant and PV = nRT : P^ 1- T^ = constant P T^ - 1 We are given that P T^ 5/2 . Comparing the exponents of T , we get: - 1 = 5 2 2 = 5 - 5 3 = 5 = 5 3 The work done by an ideal gas during an adiabatic expansion is given by: W = nR(T₁ - T₂) - 1 Since the temperature decreases by T , we have T₁ - T₂ = T . Substituting this and the value of into the work formula: W = nR T 5 3 - 1 = nR T 2 3 W = 3 2 nR T Answer: 3 2 nR T