A first$-$order system initially at $T_0$ is exposed to an ambient whose temperature varies linearly with

time according to the relation $T_{}(t)=T_1+Ct,$ where $T_1$ and $C$ are specified constants. The heat transfer

coefficient may be assumed to be constant and equal to h$.$ Determine the temperature of the system

at any time $t>0.$ Obtain the steady$-$state response of the system. If $T_0=20C,T_1=30C,C=0\mathrm{.}5\frac{C}{s}$

and $=10s$ calculate the steady$-$state response of the system. Make a plot of system temperature as

a function of time till the steady state is reached.