Assume you are performing the calibration step of Experiment 8 and you begin with 80 g of water at 20 oC and 80 g of water at 80 oC. After adding the two portions of water into your calorimeter setup and following the procedure outlined in the experiment, you determine the temperature of the mixed portions of water to be 45 oC. What is the heat capacity of the calorimeter?
qcool water + qwarm water + Ccal = 0
To determine the heat capacity of the calorimeter, we need to know the total heat gained by the water and the calorimeter during the calibration step.
First, let's calculate the heat gained by the water using the equation:
q_water = m_water * c_water * ΔT
Where:
- q_water is the heat gained by the water
- m_water is the total mass of water
- c_water is the specific heat capacity of water
- ΔT is the change in temperature of the water (final temperature - initial temperature)
Given:
- Initial temperature of the first portion of water (80 g) = 20 °C
- Initial temperature of the second portion of water (80 g) = 80 °C
- Final temperature of the mixed portions of water = 45 °C
Calculating the total heat gained by the water:
q_water = (80 g * 4.18 J/g°C * (45 °C - 20 °C)) + (80 g * 4.18 J/g°C * (45 °C - 80 °C))
Next, we need to calculate the heat lost by the calorimeter, which is equal in magnitude but opposite in sign to the heat gained by the water:
q_calorimeter = -q_water
Finally, we can determine the heat capacity of the calorimeter using the equation:
C_calorimeter = -q_calorimeter / ΔT_calorimeter
Where:
- C_calorimeter is the heat capacity of the calorimeter
- ΔT_calorimeter is the temperature change of the calorimeter during the calibration step
Since the original temperature of the calorimeter is not provided, we assume it to be at the same temperature as the first portion of water (20 °C).
Let's plug in the values and calculate:
q_calorimeter = -q_water
C_calorimeter = -q_calorimeter / ΔT_calorimeter
Please provide the value of ΔT_calorimeter (the temperature change of the calorimeter) during the calibration step, and I'll calculate the heat capacity of the calorimeter for you.