College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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![**Question:**
How many kilocalories (kcal) are required to change 1 kg of 0°C ice to 0°C water?
**Answer Box:**
[Empty text box for the answer]](https://content.bartleby.com/qna-images/question/131cad8b-b4e5-402d-8d13-746190881b41/7a7dd7bc-99ae-4802-acd8-66837dbdb95a/b78gvoa_processed.png)
Transcribed Image Text:**Question:**
How many kilocalories (kcal) are required to change 1 kg of 0°C ice to 0°C water?
**Answer Box:**
[Empty text box for the answer]
![## Understanding Heat and Phase Changes
### Heat and Temperature Change
The quantity of heat \( Q \) that changes the temperature \( \Delta T \) of a mass \( m \) of a substance is given by the formula:
\[ Q = cm \Delta T \]
where \( c \) is the specific heat capacity of the substance. For water:
\[ c = 1 \, \text{cal/g°C} = 4.2 \, \text{J/g°C} \]
This formula applies only if the substance is not changing phase.
### Heat and Phase Transitions
During phase transitions, the heat \( Q \) absorbed by a substance is used for changing its phase (e.g., melting or vaporizing) and not for changing its temperature. During this time, the temperature of the substance will not change, as illustrated in the figure below.
The quantity of heat \( Q \) that changes the phase of a mass \( m \) is given by:
\[ Q = mL \]
where \( L \) is the latent heat of fusion or vaporization of the substance. For water:
- Heat of fusion \( L_{\text{fusion}} \) = 80 cal/g = 335 J/g
- Heat of vaporization \( L_{\text{vaporization}} \) = 540 cal/g = 2260 J
### Explanation of the Graph
The graph illustrates the temperature change of a substance against the heat added. Key features include:
- **Ice Heating (from -50°C to 0°C):** Temperature increases from -50°C to 0°C using 100 cal (419 J) without phase change.
- **Melting (0°C):** Latent heat of fusion is absorbed (80 cal [335 J]) with no temperature change until it becomes water.
- **Water Heating (0°C to 100°C):** Temperature rises with additional heat.
- **Vaporization (100°C):** Latent heat of vaporization is absorbed (540 cal [2260 J]) with no temperature change until it becomes steam.
- **Steam Heating (above 100°C):** Temperature increases with more heat.
This graph provides a visual understanding of how heat energy affects phase changes and temperature in a substance like water.](https://content.bartleby.com/qna-images/question/131cad8b-b4e5-402d-8d13-746190881b41/7a7dd7bc-99ae-4802-acd8-66837dbdb95a/od03il_processed.png)
Transcribed Image Text:## Understanding Heat and Phase Changes
### Heat and Temperature Change
The quantity of heat \( Q \) that changes the temperature \( \Delta T \) of a mass \( m \) of a substance is given by the formula:
\[ Q = cm \Delta T \]
where \( c \) is the specific heat capacity of the substance. For water:
\[ c = 1 \, \text{cal/g°C} = 4.2 \, \text{J/g°C} \]
This formula applies only if the substance is not changing phase.
### Heat and Phase Transitions
During phase transitions, the heat \( Q \) absorbed by a substance is used for changing its phase (e.g., melting or vaporizing) and not for changing its temperature. During this time, the temperature of the substance will not change, as illustrated in the figure below.
The quantity of heat \( Q \) that changes the phase of a mass \( m \) is given by:
\[ Q = mL \]
where \( L \) is the latent heat of fusion or vaporization of the substance. For water:
- Heat of fusion \( L_{\text{fusion}} \) = 80 cal/g = 335 J/g
- Heat of vaporization \( L_{\text{vaporization}} \) = 540 cal/g = 2260 J
### Explanation of the Graph
The graph illustrates the temperature change of a substance against the heat added. Key features include:
- **Ice Heating (from -50°C to 0°C):** Temperature increases from -50°C to 0°C using 100 cal (419 J) without phase change.
- **Melting (0°C):** Latent heat of fusion is absorbed (80 cal [335 J]) with no temperature change until it becomes water.
- **Water Heating (0°C to 100°C):** Temperature rises with additional heat.
- **Vaporization (100°C):** Latent heat of vaporization is absorbed (540 cal [2260 J]) with no temperature change until it becomes steam.
- **Steam Heating (above 100°C):** Temperature increases with more heat.
This graph provides a visual understanding of how heat energy affects phase changes and temperature in a substance like water.
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