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?
Assume room temperature is 25 oC.
To find the heat capacity of the calorimeter, you can use the principle of heat transfer. The heat lost by the higher temperature water is equal to the heat gained by the lower temperature water and the calorimeter.
First, let's calculate the heat lost by the higher temperature water (water at 80°C):
Q_lost = m1 * c * (T1 - Tf)
Where:
m1 = mass of water at 80°C = 80 g
c = specific heat capacity of water (assumed to be 4.18 J/g°C)
T1 = initial temperature of water at 80°C = 80°C
Tf = final temperature of the mixed water = 45°C
Q_lost = 80 g * 4.18 J/g°C * (80°C - 45°C)
Q_lost = 80 g * 4.18 J/g°C * 35°C
Next, let's calculate the heat gained by the lower temperature water (water at 20°C):
Q_gained = m2 * c * (Tf - T2)
Where:
m2 = mass of water at 20°C = 80 g
T2 = initial temperature of water at 20°C = 20°C
Q_gained = 80 g * 4.18 J/g°C * (45°C - 20°C)
Q_gained = 80 g * 4.18 J/g°C * 25°C
Since the heat lost and gained are equal, we have:
Q_lost = Q_gained
80 g * 4.18 J/g°C * 35°C = 80 g * 4.18 J/g°C * 25°C
From this equation, we can cancel out the common factors like the mass and specific heat capacity of water to solve for the change in temperature (Tf - T2), which represents the heat gained by the calorimeter.
35°C = 25°C + (Tf - T2)
Tf - T2 = 35°C - 25°C
Tf - T2 = 10°C
Therefore, the change in temperature of the calorimeter is 10°C.
Finally, we can determine the heat capacity (C) of the calorimeter using the formula:
Q_gained = C * ΔT
Where:
Q_gained = heat gained by the calorimeter
ΔT = change in temperature of the calorimeter
C = Q_gained / ΔT
C = (80 g * 4.18 J/g°C * 25°C) / 10°C
Calculate the value to find the heat capacity of the calorimeter.