To determine the heat capacity of the steel, we can use the principle of conservation of energy.
First, let's calculate the heat transferred from the steel to the water.
The heat transferred from the steel can be calculated using the equation:
Q1 = mcΔT1,
where Q1 is the heat transferred from the steel, m is the mass of the steel (3 kg), c is the specific heat capacity of steel, and ΔT1 is the change in temperature of the steel.
The change in temperature of the steel (ΔT1) can be calculated as the final temperature of the calorimeter (52°C) minus the initial temperature of the steel (100°C):
ΔT1 = 52°C - 100°C = -48°C.
Substituting the given values into the equation, we have:
Q1 = (3 kg) * c * (-48°C).
Next, let's calculate the heat transferred to the water:
Q2 = mw * cw * ΔT2,
where Q2 is the heat transferred to the water, mw is the mass of the water (0.5 kg), cw is the specific heat capacity of water, and ΔT2 is the change in temperature of the water.
The change in temperature of the water (ΔT2) can be calculated as the final temperature of the calorimeter (52°C) minus the initial temperature of the water (20°C):
ΔT2 = 52°C - 20°C = 32°C.
Substituting the given values into the equation, we have:
Q2 = (0.5 kg) * cw * (32°C).
Since the total energy transferred (Q) is conserved, we can set Q1 + Q2 = 0:
(3 kg) * c * (-48°C) + (0.5 kg) * cw * (32°C) = 0.
We can rearrange this equation to solve for the heat capacity of steel (c):
(3 kg) * c * (-48°C) = - (0.5 kg) * cw * (32°C).
Simplifying:
c = - (0.5 kg) * cw * (32°C) / ((3 kg) * (-48°C)).
Given that the specific heat capacity of water (cw) is approximately 4186 J/kg°C, we can substitute this value into the equation:
c = - (0.5 kg) * 4186 J/kg°C * (32°C) / ((3 kg) * (-48°C)).
Calculating this value, we find:
c ≈ -348.3 J/kg°C.
Therefore, the heat capacity of the steel is approximately -348.3 J/kg°C. Note that the negative sign indicates that the steel loses heat energy when heated.
A 3kg piece of steel is heated to 100 degrees and placed into a calorimeter that contains 0.5kg of water at 20 degrees. The final temperature of the calorimeter was determined to be 52 degrees. What is the heat capacity of steel !?
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