You like to drink your mixture of coffee and cream very hot. However, it takes you 15 minutes to walk from the coffee house to your office, so you wonder when is best to mix the cream to the coffee. Your favourite mix is half-half, that is, half mug with hot coffee and half mug with ambient temperature cream. Your mug carries 500 cm3 of liquid and has a 50 cm2 top. The sides of the mug are very well insulated so most of the heat transfer is through the top of the mug. The heat transfer coefficient through the top of the mug is estimated to be 30 W/m2·K. If your objective is to drink the mix at the highest possible temperature in your office, should you mix the cream before leaving coffee house or when you arrive at your office? The density of both coffee and cream can be taken as 1 kg/L. The specific heat capacity for both coffee and cream is 4.18 kJ/kg·K. The coffee maker keeps the coffee at 350 K, and the ambient temperatures is 300 K. Neglect evaporative cooling effects and assume the temperature of the liquid is uniform that only changes with time. (You must solve quantitatively this problem in order to get credit for your answer.)