The difference between isothermal compressibility and adiabatic compressibility for an ideal gas is

Answer: Option B

By $$T-Ds$$  Equations at constant entropy
$$C_{p}dT=T{\frac{\partial V}{\partial T}}_{P}dP$$     and  $$C_v=-T{\left(\frac{\partial P}{\partial T}\right)}_P{\left(\frac{\partial V}{\partial T}\right)}_S$$
$$\Rightarrow \frac{C_P}{C_V}=\frac{\left(\frac{\partial P}{\partial V}\right)S}{\left(\frac{\partial P}{\partial V}\right)T}$$
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.