Answer :
Final answer:
To find the mass of water originally in the calorimeter, apply conservation of energy, with heat lost by the hot water equal to the heat gained by cooler water plus the heat absorbed by the calorimeter, using the formula q=mcδT.
Explanation:
To determine the mass of the water originally in the calorimeter, we can use the principle of conservation of energy. The heat lost by the hot water as it cools down will be equal to the heat gained by the cooler water plus the heat absorbed by the calorimeter, as both reach the final temperature. To calculate this, we need to use the formula q = mcδT, where q is the heat transferred, m is the mass, c is the specific heat capacity, and δT is the change in temperature.
Let's let m1 be the mass of the hot water, m2 be the mass of the cooler water in the calorimeter, c be the specific heat of water (4.18 J/g°C), δT1 be the change in temperature of the hot water, and δT2 be the change in temperature of the cooler water.
We know that the heat lost by the hot water (q1) can be calculated using the formula q1 = m1cδT1, where m1 = 50.75 g, δT1 = 75.6 °C - 39.4 °C, and c = 4.18 J/g°C.
The heat gained by the cooler water (q2) is q2 = m2cδT2, with δT2 = 39.4 °C - 24.1 °C.
The heat absorbed by the calorimeter is q_cal = C_calδT, where C_cal is the heat capacity of the calorimeter (26.3 J/°C) and δT is the change in temperature of the calorimeter, which is the same as the water since they reach the final temperature of 39.4 °C.
By conservation of energy, the heat lost by the hot water will be equal to the sum of the heat gained by the cooler water and the heat absorbed by the calorimeter: q1 = q2 + q_cal.
Solving for m2, we get the mass of the water originally in the calorimeter.