Imagine that your water heater has broken, but you want to take a bath. You fill your bathtub with 25kg of room-temperature water (about 25C). You figure that you can boil water on the stove and pour it into the bath to raise the temperature.

Question

Imagine that your water heater has broken, but you want to take a bath. You fill your bathtub with 25kg of room-temperature water (about 25C). 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 in order to raise the bath to body temperature (about 37C)? Assume that no heat is transferred to the surrounding environment.

Bob · Accepted Answer

4.76 kg

DrBob222 · Answer

[mass bath water x specific heat bath water x (Tfinal-Tinitial)][mass boiling water x specific heat boiling water x (Tfinal-Tinitial)] = 0
The only unknown is mass boiling water.
Use 25,000 grams for mass bath water, 4.18 J/g*C for specific heat, 37 for final T and 25 for initial T of bath water. Use 100 for initial T and 37 as final T for boiling water.