A <10.0+A> g ice cube at -15.0oC is placed in <125+B> g of water at 48.0oC. Find the final temperature of the system when equilibrium is reached. Ignore the heat capacity of the container and assume this is in a calorimeter, i.e. the system is thermally insulated from the surroundings. Give your answer in oC with 3 significant figures.
Specific heat of ice: 2.090 J/g K
Specific heat of water: 4.186 J/g K
Latent heat of fusion for water: 333 J/g
To find the final temperature when equilibrium is reached, we need to consider the heat transfer between the ice and the water.
First, let's calculate the heat absorbed by the water. We can use the following formula:
Heat absorbed = mass × specific heat × temperature change
The mass of water is given as 125 grams and the specific heat of water is 4.186 J/g K. The initial temperature of the water is 48.0oC, and we need to find the final temperature when equilibrium is reached. Therefore, the temperature change is the difference between the final temperature and the initial temperature.
Heat absorbed by water = 125 g × 4.186 J/g K × (final temperature - 48.0oC)
Next, let's consider the heat released by the ice. First, we need to calculate the heat released during the phase change from ice to water. The formula for latent heat is:
Heat released during phase change = mass × latent heat
The mass of ice is the total mass of the system minus the mass of water. The total mass is given by <10.0 + A> g, and the mass of water is 125 g.
Mass of ice = (10.0 + A) g - 125 g
Heat released during phase change = (10.0 + A - 125) g × 333 J/g
Finally, we need to calculate the heat released by the ice as it heats up from -15.0oC to 0.0oC. We can use the formula for heat:
Heat released = mass × specific heat × temperature change
The mass of ice is given as (10.0 + A) g and the specific heat of ice is 2.090 J/g K. The temperature change is 0.0oC - (-15.0oC).
Heat released by ice = (10.0 + A) g × 2.090 J/g K × (0.0oC - (-15.0oC))
Now, since the system is thermally insulated, the heat absorbed by the water must be equal to the heat released by the ice:
Heat absorbed by water = Heat released during phase change + Heat released by ice
125 g × 4.186 J/g K × (final temperature - 48.0oC) = (10.0 + A - 125) g × 333 J/g + (10.0 + A) g × 2.090 J/g K × (0.0oC - (-15.0oC))
Now, we can solve this equation to find the value of the final temperature.