Chapter 5, Problem 5.7P

Consider the steel balls of Problem 5.6, except now the air temperature increases with time as $T_{\infty }\left(t\right)=325\text{K}\text{+}at,$ where $a=0.1875\text{K/s}\text{.}$

1. Sketch the ball temperature versus time for $0\le t\le 1\text{h}\text{.}$ Also show the ambient temperature, $T_{\infty },$ in your graph. Explain special features of the ball temperature behavior.
2. Find an expression for the ball temperature as a function of time $T\left(t\right),$ and plot the ball temperature for $0\le t\le 1\text{h}\text{.}$ Was your sketch correct?