A 50.9g sample of iron, which has a specific heat capacity of 0.449·J·g−1°C−1, is put into a calorimeter (see sketch at right) that contains 100.0g of water. The temperature of the water starts off at 20.0°C. When the temperature of the water stops changing it's 23.7°C. The pressure remains constant at 1atm.Calculate the initial temperature of the iron sample. Be sure your answer is rounded to the correct number of significant digits.
Question
A 50.9g sample of iron, which has a specific heat capacity of 0.449·J·g−1°C−1, is put into a calorimeter (see sketch at right) that contains 100.0g of water. The temperature of the water starts off at 20.0°C. When the temperature of the water stops changing it's 23.7°C. The pressure remains constant at 1atm.Calculate the initial temperature of the iron sample. Be sure your answer is rounded to the correct number of significant digits.
Solution
To solve this problem, we need to use the principle of conservation of energy, which states that energy cannot be created or destroyed, only transferred. In this case, the energy is being transferred from the iron to the water in the form of heat.
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.
First, we calculate the heat gained by the water. The mass of the water is 100.0g, the specific heat capacity of water is 4.18 J/g°C (this is a known value), and the change in temperature is 23.7°C - 20.0°C = 3.7°C.
Q_water = mcΔT Q_water = (100.0g)(4.18 J/g°C)(3.7°C) = 1546.6 J
The heat gained by the water is equal to the heat lost by the iron, so Q_iron = -Q_water = -1546.6 J.
Next, we calculate the initial temperature of the iron. We know the mass of the iron is 50.9g, the specific heat capacity is 0.449 J/g°C, and the final temperature is 23.7°C.
Q_iron = mcΔT -1546.6 J = (50.9g)(0.449 J/g°C)(T_initial - 23.7°C)
Solving for T_initial, we get:
T_initial = 23.7°C - (-1546.6 J / [(50.9g)(0.449 J/g°C)]) = 23.7°C + 68.3°C = 92.0°C
So, the initial temperature of the iron sample was 92.0°C.
Similar Questions
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