Problem $2(10$ points$)-$ Mass conservation application to a control volume

The figure below shows a rigid mixing tank initially containing $3000$ lb of liquid water at $25C.$ The tank is

fitted with two inlet pipes, one delivering continuously hot water at $80C$ at a mass flow rate of $0\mathrm{.}8l\frac{b}{s}$

and the other delivering cold water at $15C$ and mass flow rate of $1\mathrm{.}2l\frac{b}{s}.$ Water exits through a single

exit pipe at a constant mass flow rate of $2\mathrm{.}5l\frac{b}{s}.$ You are interested in determining the amount of water

in the tank after one hour; you may assume that there are no leaks in the tank and the pressure of the

water in the inlet and exit ports is atmospheric. Please answer the following questions.

a$.$ Using the given figure show the boundary of the system that you would use to answer the

question presented to you. Indicate the mass and energy interactions across the boundary

and on a T$-$v diagram indicate the states corresponding to ports $(1),(2),$ and $(3).$

b$.$ Using the general equation for mass conservation, formulate an expression that can be used

to determine the instantaneous rate change of mass in the tank. Please do not perform any

computation, just show the equation that describes the rate of change for the mass in the

tank$.$ List your assumptions.

c$.$ Using your equation for part $($c$)$ compute the amount of water in the tank after one hour.