Imagine that your water heater has broken, but you want to take a bath. You fill
ID: 1060638 • Letter: I
Question
Imagine that your water heater has broken, but you want to take a bath. You fill your bathtub with 25 kg of room-temperature water (about 25 C). You figure that you can boil water on the stove and pour it into the bath to raise the temperature. How much boiling water would you need to raise the bath to body temperature (about 37 C)? Assume that no heat is transferred to the surrounding environment. (Hint: There are two different samples of water - one in the bathtub and one on the stove...treat them as separate substances)
Explanation / Answer
Q = m c T
Q = quantity of heat in joules (J)
m = mass of the substance acting as the environment in
grams (g)
c = specific heat capacity (4.19 for H2O) in J/(g oC)
T = change in temperature = Tfinal - Tinitial in oC
Heat gained by bath = - heat lost by boiling water
25kg x 4.18kJ/kgC x (37-25) = X x 4.18kJ/kgC x (37-100)
1254 = X 263.34
X = 4.76 Kg
4.76 Kg