669 cal of heat is added to 5.00 g ice at –20.0 °C. What is the final temperature of the water?
specific heat ice = ?
heat fusion water = ?
specific heat H2O = ?
To find the final temperature of the water, we need to determine the amount of heat absorbed by the ice as it changes from a solid to a liquid, and then consider the heat absorbed by the resulting liquid water to calculate its final temperature.
Here are the steps to solve the problem:
1. Calculate the heat absorbed by the ice during its phase change from solid to liquid. This is given by the equation:
Q1 = mass of ice × heat of fusion
The heat of fusion is the amount of heat required to convert 1 gram of ice at its melting point to liquid water at the same temperature. For ice, the heat of fusion is approximately 334 J/g.
Q1 = 5.00 g × 334 J/g
2. Calculate the heat absorbed by the liquid water to raise its temperature from the initial temperature to the final temperature. This is given by the equation:
Q2 = mass of water × specific heat capacity × change in temperature
The specific heat capacity of water is approximately 4.18 J/g°C.
Q2 = 5.00 g × 4.18 J/g°C × (final temperature - 0°C)
3. Use the conservation of energy principle to determine the final temperature. The total heat added to the system should be equal to the sum of Q1 and Q2.
Total heat = Q1 + Q2
669 cal = Q1 + Q2
Note: Convert the units as necessary. 1 cal = 4.18 J.
4. Solve for the final temperature by rearranging the equation and substituting the known values:
(final temperature - 0°C) = (669 cal - Q1) / (5.00 g × 4.18 J/g°C)
Remember to convert cal to J for the calculation.
5. Calculate the final temperature using the given values and solve the equation.
By following these steps, you should be able to find the final temperature of the water.