Assume you are performing the calibration step of Experiment 8 and you begin with 50 g of water at 20 oC and 50 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?

Assume room temperature is 25 oC.

Some of the water gained heat. The calorimeter gained heat. Some of the water lost heat.

heat gained + heat lost = 0
I would calculate heat lost by water, subtract heat gained by water. The difference is the heat gained by the calorimeter.

heat gained = mass water x specific heat water x (Tfinal-Tinitial).

heat lost = mass water x specific heat water x (Tfinal-Tinitial).

Take the difference. That's the heat gained by the calorimeter = heat capacity x delta (Tfinal-Tinitial).

To determine the heat capacity of the calorimeter, we need to use the principle of conservation of energy. We can calculate the amount of heat gained by the colder water and lost by the hotter water, and equate it to the amount of heat gained by the calorimeter.

Here's how to calculate the heat capacity of the calorimeter step by step:

1. Determine the heat gained by the colder water:
- Calculate the mass of the colder water by adding the masses of the two portions: 50 g + 50 g = 100 g.
- Calculate the temperature change of the colder water: 45 oC - 20 oC = 25 oC.
- Use the specific heat capacity of water (4.18 J/g°C) to calculate the heat gained by the colder water:
Heat gained = mass × specific heat capacity × temperature change
Heat gained = 100 g × 4.18 J/g°C × 25 oC = 10,450 J

2. Determine the heat lost by the hotter water:
- Calculate the temperature change of the hotter water: 80 oC - 45 oC = 35 oC.
- Use the specific heat capacity of water to calculate the heat lost by the hotter water:
Heat lost = mass × specific heat capacity × temperature change
Heat lost = 50 g × 4.18 J/g°C × 35 oC = 7,315 J

3. Assume no heat is gained or lost by the calorimeter to the surroundings. Therefore, the heat gained by the colder water and lost by the hotter water must be equal to the heat gained by the calorimeter.
- Subtract the heat lost by the hotter water from the heat gained by the colder water:
Heat gained by the calorimeter = Heat gained - Heat lost
Heat gained by the calorimeter = 10,450 J - 7,315 J = 3,135 J

4. Now we have the heat gained by the calorimeter. To calculate the heat capacity of the calorimeter, divide the heat gained by the calorimeter by the temperature change of the calorimeter:
- Calculate the temperature change of the calorimeter: 45 oC - 25 oC = 20 oC.
- Use the formula:
Heat capacity of the calorimeter = Heat gained by the calorimeter / Temperature change of the calorimeter
Heat capacity of the calorimeter = 3,135 J / 20 oC = 156.75 J/°C

Therefore, the heat capacity of the calorimeter in this experiment is approximately 156.75 J/°C.

1008 cCal

25 cCal

15 cal/C

25cal/C