A 56.9g sample of quartz, which has a specific heat capacity of 0.730·J·g−1°C−1, is put into a calorimeter (see sketch at right) that contains 150.0g of water. The temperature of the water starts off at 18.0°C. When the temperature of the water stops changing it's 22.2°C. The pressure remains constant at 1atm.Calculate the initial temperature of the quartz sample. Be sure your answer is rounded to the correct number of significant digits.
Question
A 56.9g sample of quartz, which has a specific heat capacity of 0.730·J·g−1°C−1, is put into a calorimeter (see sketch at right) that contains 150.0g of water. The temperature of the water starts off at 18.0°C. When the temperature of the water stops changing it's 22.2°C. The pressure remains constant at 1atm.Calculate the initial temperature of the quartz 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 the heat lost by the quartz 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.
First, let's calculate the heat gained by the water:
Q_water = m_water * c_water * ΔT_water Q_water = 150.0g * 4.18 J/g°C * (22.2°C - 18.0°C) Q_water = 150.0g * 4.18 J/g°C * 4.2°C Q_water = 2631.6 J
The heat lost by the quartz is equal to the heat gained by the water, so Q_quartz = Q_water = 2631.6 J.
Now, let's calculate the initial temperature of the quartz. We know that the final temperature of the quartz is 22.2°C (the same as the water), so:
Q_quartz = m_quartz * c_quartz * (T_final_quartz - T_initial_quartz)
Rearranging for T_initial_quartz gives:
T_initial_quartz = T_final_quartz - Q_quartz / (m_quartz * c_quartz) T_initial_quartz = 22.2°C - 2631.6 J / (56.9g * 0.730 J/g°C) T_initial_quartz = 22.2°C - 2631.6 J / 41.537 J/°C T_initial_quartz = 22.2°C - 63.4°C T_initial_quartz = -41.2°C
So, the initial temperature of the quartz sample was -41.2°C.
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