A 43 g ice cube at 0 �C is placed in 882 g of water at 81� C. What is the final temperature of the mixture? The specific heat of water is 4186 J/kg · �C and its latent heat of fusion is 3.33 × 105 J/kg .

Answer in units of �C

To find the final temperature of the mixture, we need to consider the energy transferred between the ice and the water until they reach thermal equilibrium. We can do this by equalizing the energy gained by the ice with the energy lost by the water.

Firstly, let's calculate the energy gained or lost by the ice during the process. We know the mass of the ice cube is 43 g and its specific heat capacity is 4186 J/kg · �C. The temperature change for the ice is the final temperature minus the melting point, which is 0 �C. So, the energy gained or lost by the ice is given by:

Energy gained or lost by the ice = mass of the ice × specific heat capacity × change in temperature
= 43 g × 4186 J/kg · �C × (final temperature - 0 �C)

Next, let's calculate the energy gained or lost by the water during the process. We know the mass of the water is 882 g and its specific heat capacity is also 4186 J/kg · �C. The temperature change for the water is the final temperature minus its initial temperature, which is 81 �C. We also need to consider the energy lost during the freezing of the ice. The latent heat of fusion for water is 3.33 × 10^5 J/kg. So, the energy gained or lost by the water is given by:

Energy gained or lost by the water = mass of the water × specific heat capacity × change in temperature + mass of the ice × latent heat of fusion

Now, we can set up an equation by equating these two values:
Energy gained or lost by the ice = Energy gained or lost by the water

43 g × 4186 J/kg · �C × (final temperature - 0 �C) = 882 g × 4186 J/kg · �C × (final temperature - 81 �C) + 43 g × 3.33 × 10^5 J/kg

Now, we can solve this equation to find the final temperature of the mixture.