What is the ratio of adiabatic compressibility to isothermal compressibility?

Solution(By Examveda Team)

By T-Ds Equations at constant entropy
$$\eqalign{ & {C_p}dT = T\frac{{\partial V}}{{\partial {T_P}}}dP{\text{ and}} \cr & {C_v} = - T{\left( {\frac{{\partial P}}{{\partial T}}} \right)_P}{\left( {\frac{{\partial V}}{{\partial T}}} \right)_S} \cr & \Rightarrow \frac{{{C_P}}}{{{C_V}}} = \frac{{\left( {\frac{{\partial P}}{{\partial V}}} \right)S}}{{\left( {\frac{{\partial P}}{{\partial V}}} \right)T}} \cr} $$
Since, $${C_P}$$  is always greater than $${C_V}$$  the ratio of isothermal compressibility and isentropic (reversible adiabatic) process is always greater than $$1 \Rightarrow $$   the difference is greater than zero.