Determining the heat capacity of a calorimeter:

Heat lost by hot water = heat gained by calorimeter + heat gained by cold water

so

-q_{hot} = q_{cal} + q_{cold}

then

-CwW2(T3-T2) = Ccal(T3-T1) + CwW1 (T3-T1)

hence

Cw W2(T2-T3) = Ccal(T3-T1) + CwW1 (T3-T1)

where: Cw = heat capacity of water (4.1858 Jg-1K-1)

Ccal = heat capacity of the calorimeter

W1 = is the weight of cold water

W2 = is the weight of hot water

T1 = is the initial temperature of the cold water

T2 = is the initial temperature of the hot water

T3 = is the maximum temperature at the instant of mixing

Method:

1. Weigh the empty calorimeter, add about 50mL of cold tap water and reweigh it to get the weight of cold water (W1).

2. Insert the digital thermometer, note the time (let this be time zero) and plot the temperature each minute for 5 minutes. Let this be T1.

3. Mix together some hot and cold water in a second beaker until the water temperature is approximately 15°C warmer than the cold water in the calorimeter. Measure out 50ml of this water in a measuring cylinder, and record the temperature.

4. Quickly add this warm water to the calorimeter, recording the exact time of mixing.

5. Swirl the water in the calorimeter and begin plotting the temperature every 30 seconds for 5 minutes.

5. From your plot determine the actual temperature rise by extrapolating to the time of mixing. Let this be T3.

6. Reweigh the calorimeter to get the weight of warm water added (W2).

7. Calculate the heat capacity of your calorimeter.