Question

A total of 565 cal of heat is added to 5.00 g of ice at -20.0°C What is the final temperature of the water? Specific heat of H, 0(5) 2.087J/g °C) Specific heat of H, 0(1) 4.184J/g °C) Heat of fusio

Answer 1

The question requires calculating the final temperature of water after adding heat to ice at a subzero temperature, taking into account the heat of fusion and the specific heat capacities for ice and water.

Step-by-step explanation:

The subject of the question involves the calculation of the final temperature of water after adding heat to ice at a subzero temperature. Initially, one must account for the energy required to raise the temperature of the ice from -20.0°C to 0°C using the specific heat of ice. Once the ice reaches 0°C, it will start to melt, requiring a certain amount of energy per gram called the heat of fusion. If any energy remains after melting the ice, it will increase the temperature of the resulting liquid water until all energy has been utilized or the water has reached the maximum temperature possible with the provided heat.

To calculate the final temperature accurately, the steps are:

The precise heat of fusion for water was not provided in the question, but typically it is approximately 79.8 cal/g, as seen in other given examples. However, without the accurate value for the heat of fusion, that step in the calculation is ambiguous.

Answer 2

The given problem involves heat transfer to ice, which undergoes a phase change into water and then heats the water to a final temperature. Firstly, we need to calculate the heat required to raise the temperature of the ice to 0°C, then the heat needed for the phase change from ice to water at 0°C (using the heat of fusion), and finally, the heat to raise the temperature of water from 0°C to the final temperature.

Step-by-step explanation:

1. Heat to raise the ice to 0°C:

`\[q_1 = m * c_{\text{ice}} * \Delta T\]`

`\[q_1 = 5.00 \, \text{g} * 2.087 \, \text{J/g°C} * (0 - (-20.0)) \, \text{°C}\]`

2. Heat for the phase change from ice to water at 0°C:

`\[q_2 = m * \Delta H_{\text{fusion}}\]`

`\[q_2 = 5.00 \, \text{g} * \text{heat of fusion}\]`

3. Heat to raise the temperature of water from 0°C to the final temperature:

`\[q_3 = m * c_{\text{water}} * \Delta T\]`

`\[q_3 = 5.00 \, \text{g} * 4.184 \, \text{J/g°C} * (\text{final temperature} - 0) \, \text{°C}\]`

The total heat added
`\(Q_{\text{total}}\)` to the system is the sum of these three quantities. Then, you can rearrange the equation and solve for the final temperature using the total heat added and the calculated heats for the individual processes. After finding the total heat added, equate it to the sum of \
`(q_1\), \(q_2\), and \(q_3\)` to solve for the final temperature of the water.