In the laboratory, a student heats 96.27 grams of zinc to 98.06 °C and then drops it into a cup containing 76.46 grams of water at 22.44 °C. She measures the final temperature to be 30.31 °C.
Using the accepted value for the specific heat of zinc (See the References tool), calculate the calorimeter constant.
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To calculate the calorimeter constant, we need to use the principle of conservation of energy, specifically the equation for heat transfer:
Q = mcΔT
where Q is the heat transferred, m is the mass of the substance, c is the specific heat capacity of the substance, and ΔT is the change in temperature.
In this case, we can calculate the heat transferred from the zinc to the water and cup, and equate it to the heat gained by the water and cup.
First, let's calculate the heat transferred from the zinc:
Qzinc = mzinc × czinc × ΔTzinc
where mzinc is the mass of the zinc, czinc is the specific heat capacity of the zinc, and ΔTzinc is the change in temperature of the zinc.
mzinc = 96.27 g
czinc = specific heat capacity of zinc (you can find this value in the References tool)
ΔTzinc = 30.31 °C - 98.06 °C
Now, let's calculate the heat gained by the water:
Qwater = mwater × cwater × ΔTwater
where mwater is the mass of the water, cwater is the specific heat capacity of water, and ΔTwater is the change in temperature of the water.
mwater = 76.46 g
cwater = specific heat capacity of water (you can find this value in the References tool)
ΔTwater = 30.31 °C - 22.44 °C
Finally, we can equate Qzinc and Qwater and solve for the calorimeter constant, Cc:
Qzinc = Qwater + Cc
Solving for Cc:
Cc = Qzinc - Qwater
Substituting the calculated values, you can now determine the calorimeter constant.