Answer to Question #83963 in Physical Chemistry for Yamini kadian

Question

Adiabatic reversible expansion of a monoatomic gas (M) and a diatomic gas (D) at an initial temperature Ti.
has been carried out independently from initial volume V1, to final volume V2. The final tempratre (Tm for monoatomic and Td for diatomic) attained will be
(b) Tm < Td <Ti
(c) Tm >Td >Ti
(a) Tm=Td>Ti
(d) Td <Tm <Ti

Answer 1

Solution:

The reversible adiabatic process for an ideal gas is described by the Poisson equation. Since the temperature is variable in the adiabatic process, the Boyle – Mariotte law requires an amendment, which Poisson designated as the coefficient k and expressed through the heat capacity ratio. For non-relativistic non-degenerate monatomic ideal k = 5/3, for diatomic k = 7 / 5.

c) Tm >Td >Ti