A tank with its top open to the atmosphere contains liquid methanol $,$ molecular weight $32\frac{g}{m}ol)$ at the bottom of the tank. The tank is maintained at $30C.$ The diameter of the cylindrical tank is $1\mathrm{.}0m,$ the total height of the tank is $3\mathrm{.}0m,$ and the liquid level at the bottom of the tank is maintained at $0\mathrm{.}5m.$ The gas space inside the tank is stagnant and the $CH3OH$ vapors are immediately dispersed once they exit the tank.

At $30C,$ the vapor pressure exerted by liquid $CH3OH$ is $163mmHg$ and at $40C$ the $CH3OH$ vapor pressure is $265mmHg.$ We are concerned that this open tank may be emitting a considerable amount of $CH3OH$ vapor.

a$.$ What is the emission rate of $CH3OH$ vapor from the tank in units of $kgCH3OH/$day when the tank is at a temperature of $30C?$ State all assumptions and boundary conditions.

b$.$ If the temperature of the tank is raised to $40C,$ what is the new methanol emission rate?