To find the final temperature, we need to calculate the heat lost by the silver bear and cup and the heat gained by the water in the calorimeter.
The heat lost by the silver bear and cup can be calculated using the formula:
Q = mcΔT
Where:
Q = heat lost
m = mass
c = specific heat
ΔT = change in temperature
For the silver bear:
Q_silver = 289g * 0.234 J/(g*K) * (95.5 - Teq)
For the aluminum cup:
Q_aluminum = 229g * 0.910 J/(g*K) * (95.5 - Teq)
The heat gained by the water can be calculated using the formula:
Q_water = m * c * ΔT
Q_water = 265g * 4190 J/(kg*K) * (Teq - 21.5)
Since energy is conserved in the system, the heat lost by the silver bear and cup plus the heat lost by the aluminum cup must equal the heat gained by the water:
Q_silver + Q_aluminum = Q_water
289g * 0.234 J/(g*K) * (95.5 - Teq) + 229g * 0.910 J/(g*K) * (95.5 - Teq) = 265g * 4190 J/(kg*K) * (Teq - 21.5)
Solve for Teq:
(67.726 J/K * (95.5 - Teq)) + (208.39 J/K * (95.5 - Teq)) = (1110.85 J/K * (Teq - 21.5))
67.726(95.5 - Teq) + 208.39(95.5 - Teq) = 1110.85(Teq - 21.5)
6473.93 - 67.726Teq + 20003.945 - 208.39Teq = 1110.85Teq - 23844.925
-276.116Teq = -16875.985
Teq ≈ 61.18 degrees C
Therefore, the final temperature Teq of the water, cup and bear when they reach thermal equilibrium is approximately 61.18 degrees C.
A 289 g silver figure of a polar bear is dropped into the 229 g aluminum cup of a well-insulated calorimeter containing 265 g of liquid water at 21.5 degrees C. The bear's initial temperature is 95.5 degrees C. The specific heats of silver, aluminum, and liquid water are, respectively, 234 J/(kgxk), 910 J/(kgxK), and 4190 J/kgxK). What is the final temperature Teq of the water, cup and bear when they reach thermal equilibrium?
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1 answer