1. The problem statement, all variables and given/known data (a) In an espresso coffee machine, steam at 100 °C is passed into milk to heat it. Calculate (i) the energy required to heat 150 g of milk from room temperature (20 °C) to 80 °C, (ii) the mass of steam condensed. (b) A student measures the temperature of the hot coffee as it cools. The results are given below: A friend suggests that the rate of cooling is exponential. (i) Show quantitatively whether this suggestion is valid. (ii) Estimate the temperature of the coffee after a total of 12 min. Specific heat capacity of milk = 4.0 kJ kg-1 K-1 Specific heat capacity of water = 4.2 kJ kg-1 K-1 Specific latent heat of steam = 2.2 MJ kg-1 Answers: (a) (i) 3.6 * 104 J, (ii) 15.8 g 2. The attempt at a solution (a) (i) ΔQ = mcΔθ = 0.15 kg * 4000 J kg-1 K-1 * (80-20 °C) = 36 000 J -- the energy required to heat 150 g of milk from room temperature of 20 degrees to 80 degrees. (a) (ii) ΔQ = ml → to find mass m = ΔQ / l = 36 000 J / 2.2 * 106 J kg-1 = 0.016 kg or 16.4 g. Which is wrong. What did I miss? (b) (i) Can't say that it's exponential, since the increase is not the same in percentage. (b) (ii) The temperature should be 29 °C, because we have a difference of two twice and a difference of one once. So, I guess every difference should be two times the number: 2 x 2, 2 x 1, 2 x 0. In sum: what's missing in (a) (ii) and is my logic in (b) (i-ii) correct?