Question #42525

A closed cubical container of side length $H$ is completely filled with a liquid of total mass $M$ and density $\rho$. The container is initially at rest, and the liquid is at its normal boiling point $T_0$ with the pressure at the top-front edge ($x=0, y=0$) being $P_0$. The container is then given a constant horizontal acceleration $a$ in the $-x$ direction (where $y$ is the downward vertical direction). The rate of change of the boiling point with pressure is a constant $\alpha$ (i.e., $\frac{dT}{dP} = \alpha$). To maintain the liquid at the verge of boiling everywhere and to vaporize a small uniform mass fraction $f$ of the liquid throughout the volume, a total heat $Q$ must be supplied. Assume the pressure at the top-front edge remains $P_0$, and the volume of vapor formed is negligible. Given $C$ is the specific heat capacity of the liquid and $L_v$ is the latent heat of vaporization, find the total heat $Q$ supplied.