In Column $-I$ processes and in Column $-II$ formulas of work are given. Match them appropriately:

Column $-I$	Column $-II$
$(a)$ Isothermal process	$(i)$ $W = \frac{\mu R(T_1 - T_2)}{\gamma - 1}$
$(b)$ Adiabatic process	$(ii)$ $W = P\Delta V$
	$(iii)$ $W = 2.303\mu RT \log_{10} \left( \frac{V_2}{V_1} \right)$

(A) For an isothermal process,the temperature $T$ remains constant. The work done is given by $W = \int_{V_1}^{V_2} P dV = \int_{V_1}^{V_2} \frac{\mu RT}{V} dV = \mu RT \ln \left( \frac{V_2}{V_1} \right) = 2.303 \mu RT \log_{10} \left( \frac{V_2}{V_1} \right)$. Thus,$(a)$ matches with $(iii)$.
For an adiabatic process,the work done is given by $W = \frac{\mu R(T_1 - T_2)}{\gamma - 1}$. Thus,$(b)$ matches with $(i)$.
Therefore,the correct matching is $(a-iii, b-i)$.