When a diatomic gas (rigid) undergoes adiabatic change, its pressure (P) and temperature (T) are related as P T ^ c . The value of c is

Step-by-step solution

For an adiabatic process in a diatomic gas, PV^ = constant and P^ 1- T^ = constant are key relations. From the latter, P^ 1- T^ = constant implies P T^ /( -1) . Comparing with P T^c yields c = -1 . For a rigid diatomic gas, the adiabatic index is = 1 + 2 f , where f = 5 degrees of freedom. Thus, = 7 5 . Substituting this into the expression for c gives c = 7/5 (7/5)-1 = 7/5 2/5 = 7 2 = 3.5 . The value of c is B .