Question

You have 4.6 kg of water in an insulated container. You add 1 kg of ice at -22 °C to the water and the mix reaches a final, equilibrium temperature of 17 °C. The specific heats of ice and water are 2.10 ×103 J/kg⋅ C° and 4.19 ×103 J/kg⋅ C°, respectively, and the latent heat of fusion for water is 3.34 ×105 J/kg. Calculate the initial temperature of the water, in degrees Celsius.

Answer 1

To find the initial temperature of the water, we can use the principle of conservation of energy. The heat gained by the water and ice mixture is equal to the heat lost by the hot water. The heat gained can be calculated as the sum of the heat needed to melt the ice and the heat needed to raise the temperature of the ice-water mixture to the final temperature.

Step-by-step explanation:

To find the initial temperature of the water, we can use the principle of conservation of energy. The heat gained by the water and ice mixture is equal to the heat lost by the hot water. The heat gained can be calculated as the sum of the heat needed to melt the ice and the heat needed to raise the temperature of the ice-water mixture to the final temperature.

First, let's calculate the heat needed to melt the ice. The latent heat of fusion for water is 3.34 × 10^5 J/kg, and we have 1 kg of ice. Therefore, the heat needed to melt the ice is 1 kg * 3.34 × 10^5 J/kg = 3.34 × 10^5 J.

Next, let's calculate the heat needed to raise the temperature of the ice-water mixture to the final temperature. We know the specific heat capacity of ice is 2.10 × 10^3 J/kg⋅C°, and the specific heat capacity of water is 4.19 × 10^3 J/kg⋅C°.