Heat and Temperature

[IUBritt09]

1. The problem statement, all variables and given/known data

Swimming pool A contains twice as much water as swimming pool B. The water in each pool started at air temperature. Which pool had more heat transferred to it?

Currently: Swimming pool A is at 29 degrees celsius
Swimming pool B is at 30 degrees celsius
Air temperature is 20 degrees celsius


2. Relevant equations

Q is proportional to A

3. The attempt at a solution

If Q is proportional to A, then A should have had more heat transferred to it since it has a larger cross-sectional area. (My homework is multiple choice, a, b, or both. You are penalized for guessing so I just want to make sure that my thinking is correct before I select an answer. Any guidance would be greatly appreciated!)

[Dick]

The heat transfered is proportional to the mass of the water times the heat capacity times the change in temperature. What does that tell you? Cross-sectional area has nothing to do with this.

[IUBritt09]

Since pool A is twice as large as pool B, its mass is larger, and pool A's heat capacity is also larger because the value of heat capacity is proportional to the amount of material in the object, and it's change in temperature is only a degree less than that of pool B. Therefore, A had more heat transfer.

[Dick]

No, I'm talking about heat capacity per unit mass. If the mass of A is m then the mass of B is m/2. So if heat capacity is can you write expressions for the heat transfer for A and B? Can you show one is larger than the other? If the temperature change for A vs B had been different, then the answer might be different.