You have an ice cube (H2O) that weighs 5 grams and is at a temperature of -10 degrees Celsius. How much heat energy(in joules) is required to melt the ice cube and raise the temperature of the resulting liquid water to 15 degrees Celsius?
A. 1803 J
B. 2088.5 J
C. 257.5 J
D. 418.2 J
See later post on how to solve.
To calculate the amount of heat energy required to melt the ice cube and raise the temperature of the resulting water, we need to consider two processes: the heat energy required to melt the ice and the heat energy required to raise the temperature of the liquid water.
1. Heat energy to melt the ice:
The heat energy required to melt one gram of ice at 0 degrees Celsius is 334 J. Since the ice cube weighs 5 grams, the heat energy required to melt it can be calculated as follows:
Heat energy to melt ice = 5 grams * 334 J/gram = 1670 J
2. Heat energy to raise the temperature of the liquid water:
The specific heat capacity of water is 4.184 J/g °C. So, to raise the temperature of 5 grams of water from -10 degrees Celsius to 15 degrees Celsius, we need to calculate the heat energy using the formula:
Heat energy = mass * specific heat capacity * change in temperature
Heat energy to raise the temperature = 5 grams * 4.184 J/g °C * (15 °C - (-10 °C)) = 5 grams * 4.184 J/g °C * 25 °C = 523 J
Now, to find the total heat energy required, we add the heat energy required to melt the ice and the heat energy required to raise the temperature of the water:
Total heat energy = Heat energy to melt ice + Heat energy to raise the temperature = 1670 J + 523 J = 2193 J
Now comparing the answer choices:
A. 1803 J: This is less than 2193 J, so it cannot be the correct answer.
B. 2088.5 J: This is also less than 2193 J, so it cannot be the correct answer.
C. 257.5 J: This is much less than 2193 J, so it cannot be the correct answer.
D. 418.2 J: This is less than 2193 J, so it cannot be the correct answer.
Therefore, none of the provided options match the calculated total heat energy of 2193 J.