A rigid diatomic gas undergoes adiabatic change. Its pressure P and temperature T are related as P T^x where x is

Step-by-step solution

For an adiabatic process, the relation between pressure and volume is PV^ = constant . Using the ideal gas equation PV = nRT , we can replace V with nRT P to get: P ( T P )^ = constant P^ 1- T^ = constant P T^ -1 Comparing this with P T^x , we get x = -1 . For a rigid diatomic gas, the number of degrees of freedom is f = 5 . The ratio of specific heats is = 1 + 2 f = 1 + 2 5 = 7 5 . Substituting the value of into the expression for x : x = 7 5 7 5 - 1 = 7 5 2 5 = 7 2 = 3.5 Answer: 3.5