Answer:
The initial temperature of the quartz sample was 16.3 °C.
Step-by-step explanation:
The heat lost by the quartz sample is equal to the heat gained by the water and the calorimeter. Therefore:
q_quartz = q_water + q_calorimeter
The heat lost by the quartz sample can be calculated using the equation:
q_quartz = m_quartz × c_quartz × ΔT_quartz
where m_quartz is the mass of the quartz sample, c_quartz is the specific heat capacity of quartz, and ΔT_quartz is the change in temperature of the quartz sample.
The heat gained by the water and calorimeter can be calculated using the equation:
q_water + q_calorimeter = (m_water + m_calorimeter) × c_water × ΔT_water
where m_water is the mass of the water, m_calorimeter is the mass of the calorimeter, c_water is the specific heat capacity of water, and ΔT_water is the change in temperature of the water and calorimeter.
Since the pressure is constant and no work is being done, we can assume that the total heat gained by the water and calorimeter is equal to the heat lost by the quartz sample. Therefore:
m_quartz × c_quartz × ΔT_quartz = (m_water + m_calorimeter) × c_water × ΔT_water
Substituting the given values, we get:
(0.0548 g) × (0.730 J/g·°C) × (T_i - 26.4 °C) = (200.0 g + 100.0 g) × (4.184 J/g·°C) × (26.4 °C - 23.0 °C)
Simplifying and solving for Ti, we get:
Ti = 16.3 °C (rounded to 2 significant digits)
Therefore, the initial temperature of the quartz sample was 16.3 °C.