Coffee virtual lab

Question

An eccentric Chemistry teacher orders a coffee to be made that is at exactly 78.6 Celsius.  He requires that you start with 189 mL of coffee heated to 91.3 celsius.  You must add Milk from the fridge at 3.2 Celsius to make the perfect cup of coffee.  How many milliliters of milk must you add?  (round to tenths place)  note:  It can be assumed that coffee and milk have the same specific heat capacity of liquid water.  Good luck Barista!

Answer 1

Specific heat capacity of H2O = C = 4.184 J/gº

The heat lost by the hot coffee MUST equal the heat gained by the cold milk.

For the problem, we will use the equation q = mC∆T where

m = mass

C = specific heat

∆T = change in temperature

Heat lost by coffee = q = mC∆T = (189 ml x 1 g/ ml)(4.184 J/gº)(91.3 - 78.6) = (189 g)(4.184 J/gº)(12.7º) = 10,043 J

Heat gained by milk = q = 10,043 J = mC∆T = (x g)(4.184 J/gº)(78.6 - 3.2) = 315.4 x

Solving for x (mass of milk) we have...

10,043 = 315.4 x

x = 31.8 mls = 31.8 g

Answer 2

Milk and coffee have the specific heat and density of water. The loss of energy of the coffee will be gained by the milk leading to the final temperature.

m_cc(T_ci - T_f)) = m_mc(T_f - T_mi) where i means initial, f means final and m and c are milk and coffee. We can make the equation in terms of volume:

V_cρc(T_ci - T_f) = V_mρc(T_f - T_mi) which leads to

V_m = V_c (T_ci - T_f)/(T_f - T_m) You can use °C because T's are differences.