Physics

Problem

A cup of coffee is served at

90^{\circ}\mathrm{C}

in a room whose air is maintained steadily at

25^{\circ}\mathrm{C}

. Five minutes later the temperature of the coffee is found to be

70^{\circ}\mathrm{C}

. Assume the temperature

T(t)

of the coffee (in

^{\circ}\mathrm{C}

) at time

t

minutes satisfies the relation

T(t)=T_s+(T_0-T_s)e^{-kt}

. (i) Using the information given, calculate the cooling constant

k

(correct to four significant figures). (ii) Hence determine the time, to the nearest minute, required for the coffee to cool to

40^{\circ}\mathrm{C}