$9\mathrm{.}5$ An electrical resistor in a direct current generates energy internally at a rate of $0\mathrm{.}01$

W$.$ It has a mass of $5{10}^{-5}kg,$ a surface area of $4{10}^{-5}{m}^2,$ and a heat capacity of

$300\frac{J}{k}g*C.$ Before the current starts flowing, it is at the temperature of the sur$-$

roundings $(25C).$ The heat transfer coefficient between the resistor and the sur$-$

rounding air is $20\frac{J}{s}*m^2*C.$

a$.$ Develop the mathematical model for the temperature $T$ of the resistor.

b$.$ What temperature will the resistor ultimately reach? Using the notion that the

resistor will reach a steady state after five time constants, about how long will

it take for the resistor to reach its ultimate temperature?

c$.$ Obtain an analytical solution for $T(t)$ of the resistor. When will the temperature

of the resistor reach $30C?$

PLEASE WRITE NEAT AND EXPLAIN EACH STEP PLEASE $!$