Calculate the weight in kg of a block of aluminum at 93 °C placed in 3.3 kg of water at 25 °C if the final temperature becomes 33 °C. The heat capacity of water = cw = 4184 J/kg°C, and the heat capacity of Aluminum = cAl = 900 J/kg°CRound answer to the nearest two decimal places
Question
Calculate the weight in kg of a block of aluminum at 93 °C placed in 3.3 kg of water at 25 °C if the final temperature becomes 33 °C. The heat capacity of water = cw = 4184 J/kg°C, and the heat capacity of Aluminum = cAl = 900 J/kg°CRound answer to the nearest two decimal places
Solution
To solve this problem, we need to use the principle of conservation of energy, which states that the heat lost by the aluminum block will be equal to the heat gained by the water.
The formula for heat transfer is Q = mcΔT, where:
- Q is the heat transferred,
- m is the mass,
- c is the specific heat capacity, and
- ΔT is the change in temperature.
Let's denote the mass of the aluminum block as mAl.
The heat lost by the aluminum block is QAl = mAl * cAl * ΔTAl, where:
- ΔTAl = Tinitial_Al - Tfinal = 93°C - 33°C = 60°C.
The heat gained by the water is Qw = mw * cw * ΔTw, where:
- ΔTw = Tfinal - Tinitial_w = 33°C - 25°C = 8°C.
Setting QAl = Qw, we get:
mAl * cAl * ΔTAl = mw * cw * ΔTw.
Substituting the given values:
mAl * 900 J/kg°C * 60°C = 3.3 kg * 4184 J/kg°C * 8°C.
Solving for mAl, we get:
mAl = (3.3 kg * 4184 J/kg°C * 8°C) / (900 J/kg°C * 60°C).
Now, calculate the above expression to find the mass of the aluminum block. Round your answer to the nearest two decimal places.
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