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?
heat lost by hot water is
q1 = mass x specific heat x (Tfinal-Tinitial).
heat absorbed by the cold water is
q2 = mass x specific heat x (Tfinal-Tinitial).
The difference of the two is the heat absorbed by the calorimeter and delta H/delta T = heat capacity of the calorimeter.
To determine the heat capacity of the calorimeter, we need to use the principle of conservation of energy. The heat gained by the cooler water (Q_cooler) must be equal to the heat lost by the hotter water (Q_hotter) when they are mixed together.
The equation that relates heat gained or lost by an object is Q = m * c * ΔT, where Q is the heat, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
1. Calculate the heat lost by the hotter water (Q_hotter):
Q_hotter = (mass of hotter water) * (specific heat capacity of water) * (initial temperature of hotter water - final temperature of mixed water)
Q_hotter = 50 g * 4.18 J/g°C * (80°C - 45°C)
2. Calculate the heat gained by the cooler water (Q_cooler):
Q_cooler = (mass of cooler water) * (specific heat capacity of water) * (final temperature of mixed water - initial temperature of cooler water)
Q_cooler = 50 g * 4.18 J/g°C * (45°C - 20°C)
3. Since the system is isolated, the heat lost by the hotter water is equal to the heat gained by the cooler water:
Q_hotter = Q_cooler
4. So, we have the equation:
50 g * 4.18 J/g°C * (80°C - 45°C) = 50 g * 4.18 J/g°C * (45°C - 20°C)
5. Now, we can solve for the specific heat capacity of the calorimeter (c_calorimeter):
c_calorimeter = (50 g * 4.18 J/g°C * (80°C - 45°C)) / (50 g * (45°C - 20°C))
Performing the calculations, we find:
c_calorimeter ≈ 0.837 J/°C
Therefore, the heat capacity of the calorimeter is approximately 0.837 J/°C.