One mole of an ideal gas expands adiabatically from an initial state ( T A , V 0 ) to final state ( T f , 5 V 0 ) . Another mole of the same gas expands isothermally from a different initial state ( T B , V 0 ) to the same final state ( T f , 5 V 0 ) . The ratio of the specific heats at constant pressure and constant volume of this ideal gas is γ . What is the ratio T A T B ?

Step-by-step solution

As we know for an Adiabatic process T V γ - 1 = Constant . ⇒ T A V 0 γ - 1 = T f 5 V 0 γ - 1                         . . . i For Isothermal process T B = T f                         . . . ii Dividing equation i by equation ii , we get ⇒ T A T B = 5 γ - 1