A tank contains $5$m$^3$ of water up to the end as shown below. The temperature of the water in the tank is initially at $25$C$.$ If the valve is suddenly opened to supply water at a rate of $0\mathrm{.}1$ m$^3/$hr and temperature of $75$C$.$ Calculate the temperature in the tank as a function of time. What is the steady state temperature in the tank?