Exercise

A cup of coffee is taken from a coffeemaker at 98$^\circ$C and left on the office table. In the air-conditioned office, the temperature is held at 20$^\circ$C. After 5 minutes, the coffee's temperature is 38$^\circ$C.

1.

How much longer will it take the coffee to loose its taste quality, i.e., to cool down to the temperature of 22$^\circ$C?

2.

Assume the coffee is left on the table of an outside cafe on a hot summer day when the temperature is 35$^\circ$C and on a cold winter day when the temperature is 5$^\circ$C. Get the expression for the coffee temperature as a function of time for these cases in form (5).

3.

Plot the graphs T versus t for the all three environments using the same coordinate axes.

4.

From the graphs, make an estimate when the coffee should be drunk in each situation (in office, in winter cafe, in summer cafe) if the coffee is supposed to be best at temperature 60$^\circ$C.