# At what rate is energy being removed in the following case?A 215 g aluminum cup holds and is in thermal equilibrium with 852 g of water at 82°C. The combination of cup and water is cooled...

At what rate is energy being removed in the following case?

A 215 g aluminum cup holds and is in thermal equilibrium with 852 g of water at 82°C. The combination of cup and water is cooled uniformly so that the temperature decreases by 1.4°C per minute. At what rate is energy being removed?

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### 1 Answer

A 215 g aluminum cup holds and is in thermal equilibrium with 852 g of water at 82 C. The combination of cup and water is cooled uniformly so that the temperature decreases by 1.4 C per minute. The rate at which heat has to be removed to accomplish this is required.

The specific heat of water is 4.178 J/g*C and the specific heat of aluminum is 0.902 J/g*C

To decrease the temperature of 215 g of aluminum and 852 g of water by 1 C, the heat that has to be removed is 215*0.902 + 852*4.178 = 3753.86 J. As the rate of cooling in 1.4 C/minute the amount of heat to be removed in a minute is 5255.02 J.

During the cooling process heat is being removed at 5255.02 J/minute.