$2-2-15$ A rigid insulated tank contains $2$ kg of a gas at $300$ K and $100$ kPa $.$ A $1$ kW internal heater is turned on$.($a$)$ Determine the rate of change of total stored energy $(d\frac{E}{d}t).($b$)$ If the internal energy of the gas is related to the temperature by $u=1\mathrm{.}1T(k\frac{J}{k}g),$ where $T$ is in Kelvin. determine the rate of temperature increase.