4. You purchase a 100 °C, 14 oz. cup of coffee at a coffee shop on a -15 °C day. You want to drink the coffee at your house, which is a 10-minute walk from the shop. You prefer 2 oz. of cream in your coffee and are debating whether you should add it at the coffee shop or when you get home. Assume that adding cream at room temperature 25 °C to the hot coffee decreases its temperature to a volume-weighted average of the coffee temperature and cream temperature. Should you add the cream at the coffee shop or immediately when you get home such that the coffee is the hottest before your drink it? The initial temperature of the coffee is 100 °C and the convection coefficient during your walk is25 W/m²-K. Use the thermal properties of water for the coffee (k = 0.6 W/m-K, p = 1000 kg/m³, and Cp = 4180 J/kg-K). Assume the coffee is in a paper cup with a thermal resistance of 0.05 m-K/W (per unit length of the cup) and inside diameter of 7 cm. Assume heat leaves only through the sides of the cup (not the top or bottom) by convection and that the inside surface of the paper cup is equal to the coffee temperature. Hint: start by drawing a control volume around the coffee and performing an energy balance assuming lumped capacitance.