Column I Column II
a.	Joule Thomson coefficient	p.	\[{{\left( \frac{\partial U}{\partial V} \right)}_{T}}=0\]
b.	Kirchhoff’s Equation	q.	\[\left( \frac{2a}{RT}-b \right)\]
c.	Ideal gas	r.	\[{{\left( \frac{\partial \Delta H}{\partial T} \right)}_{P}}=\Delta Cp\]
d.	Inversion temperature.	s.	\[{{\left( \frac{\partial T}{\partial P} \right)}_{H}}=\frac{-{{(\partial H/\partial P)}_{T}}}{Cp}\]

(A) \[(a\to s)(b\to r)(c\to p)(d\to q)\]
(B) \[(a\to r)(b\to s)(c\to p)(d\to q)\]
(C) \[(a\to p)(b\to r)(c\to s)(d\to q)\]
(D) \[(a\to q)(b\to p)(c\to r)(d\to s)\]

Hint:We have to match the column-I with column-II according to the proper options. All the formulas which are mentioned in the question are related to behavior of gases at different temperature, pressure and volume.

Complete step by step solution:
> The Joule–Thomson effect defines the temperature change of a real gas or a liquid when it is forced through a porous plug while keeping it insulated. So, that no heat is exchanged with the environment.
Joule Thomson coefficient = \[{{\left( \frac{\partial T}{\partial P} \right)}_{H}}=\frac{-{{(\partial H/\partial P)}_{T}}}{Cp}\]
> Kirchhoff equations, named after Gustav Kirchhoff, explains the motion of a rigid body in an ideal fluid. Similarly represent all other torques and forces acting on the body. The integration is done over the fluid-exposed share of the body's surface.
Kirchhoff’s Equation = \[{{\left( \frac{\partial \Delta H}{\partial T} \right)}_{P}}=\Delta Cp\]
> An ideal gas is composed of many randomly moving point particles that are not subject to interparticle interactions. Ideal gas is an assumed gas whose molecules occupy minor space and have no interactions themselves, and which accordingly obeys the all gas laws exactly.
Ideal gas = \[{{\left( \frac{\partial U}{\partial V} \right)}_{T}}=0\]
> The inversion temperature is the critical temperature below which a non-ideal gas that is expanding at constant enthalpy will practice a decrease in temperature, and above which will experience an increase in temperature.
Inversion temperature = \[\left( \frac{2a}{RT}-b \right)\]

> So, the correct option is A,\[(a\to s)(b\to r)(c\to p)(d\to q)\].

Note:The volume of a gas sample is directly proportional to its absolute temperature at constant pressure is called Charles’s law.
> The volume of a gas is inversely proportional to its pressure when temperature is constant is called Boyle’s law.
> Under the same conditions of temperature and pressure, equal volumes of all gases containing the same number of molecules is called Avogadro’s law.