Answer
(a) 20ºC; The temperature of the surroundings
(b) At T=160ºC
Work Step by Step
(a) We can see that the graph of time vs temperature is asymptotic to the line T = 20ºC. As the time increases, the temperature of the object gets more and more closer to 20ºC which therefore is its limit as ${h \to \infty}$. This is the temperature of the surroundings because temperature of any object approaches the temperature of its surroundings following $Newton's$ $law$ $of$ $cooling.$
(b) According to $Newton's$ $law$ $of$ $cooling$, the rate of change of temperature of an object is directly proportional to the difference between its temperature and the temperature of its surroundings. This difference is maximum when T=160ºC. It can also be seen from the graph that the slope of the curve -and hence the rate of change of temperature- is greatest at this point
