A power transistor mounted on a finned heat sink can be modeled as a spatially isothermal object with internal heat generation and an external convection resistance.

Consider such a system of mass $M,$ specific heat $c,$ and surface area $A_s,$ which is initially in equilibrium with the environment at $T_{}.$ Suddenly, the device is energized such that a constant heat generation $E_g^{}($ W $)$ occurs.

Derive the temperature response of the device, $\frac{}{{}_i},$ in terms of $R,C,$ and $t,$ where $-=T-T()$ and $T()$ is the steady$-$state temperature corresponding to $t$;${}_i=T_i-T()$;$T_i=$ initial temperature of device; $R=$ thermal resistance $\frac{1}{\frac{?}{?}}$bar $(h)A_s$; and $C=$ thermal capacitance $Mc.$ Use this expression to answer the following.

A device which generates $100W$ of heat is mounted on an pure aluminum heat sink weighing $0\mathrm{.}35kg$ and reaches a temperature of $100C$ in ambient air at $20C$ under steady$-$state conditions. If the device is initially at $20C,$ what temperature, in $C,$ will it reach $5$min after the power is switched on$?$