Question #42137

A parallel plate capacitor of initial capacitance $C_0$ is connected to a constant voltage source $V$. The space between the plates is completely filled with a non-polar liquid dielectric of initial dielectric constant $K_0$ at temperature $T_0$. The liquid has a volume expansion coefficient $\gamma$. The capacitor plates are held rigidly at a constant separation, and a small reservoir allows the liquid to expand out so the volume between the plates remains constant. Assuming the electric susceptibility of the liquid is directly proportional to its density, what is the magnitude of the change in the electrostatic energy stored in the capacitor when the temperature is increased by a small amount $\Delta T$? (Assume $\gamma \Delta T \ll 1$)