A 300-g aluminum cup contains 700 g of water in thermal equilibrium with the cup at 60°C. The combination of cup and water is cooled uniformly so that the temperature decreases by 2.2°C per minute. At what rate is energy being removed? Express your answer in watts.

Question

Zion Johns

Chemistry

30 January, 17:04

A 300-g aluminum cup contains 700 g of water in thermal equilibrium with the cup at 60°C. The combination of cup and water is cooled uniformly so that the temperature decreases by 2.2°C per minute. At what rate is energy being removed? Express your answer in watts.

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Answers (1)

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Natalia · Answer 1

117.3 W is being removed.

Explanation:

The heat removed can be calculated as:

Q = m*c*ΔT

Where m is the mass, c is the specific heat and ΔT is the temperature variation. Because there're two components:

Q = mwater*cwater*ΔT + maluminum*caluminum*ΔT

Q = (mwater*cwater + maluminum*caluminum) * ΔT

Searching in a thermodynamic table:

cwater = 4.184 J/g°C

caluminium = 0.9 J/g°C

In 1 minute, the temperature decreases 2.2°C, so ΔT = - 2.2°C

Q = (700*4.184 + 300*0.9) * (-2.2)

Q = - 7037.36 J

The rate of energy is the potency (P), which is the heat divided by the time. So, for 1 minute (60 s):

P = - 7037.36/60

P = - 117.3 J/s

P = - 117.3 W

The minus signal indicates that the energy is being removed.