Question
The specific heat of water is 4.18 J/(gi°C) and that of wood is 1.97 J/(gi°C). Which statement is correct?
Regardless of mass, wood will heat up less than water if the same heat is added.
Given equal masses, wood will heat up less than water if the same heat is added.
Given equal masses, water will heat up less than wood if the same heat is added.
Regardless of mass, water will heat up less than wood if the same heat is added.
Regardless of mass, wood will heat up less than water if the same heat is added.
Given equal masses, wood will heat up less than water if the same heat is added.
Given equal masses, water will heat up less than wood if the same heat is added.
Regardless of mass, water will heat up less than wood if the same heat is added.
Answers
GPT-4o mini
To understand how specific heat capacity affects the temperature change of substances when the same amount of heat is added, we can use the formula:
\[ Q = mc\Delta T \]
where:
- \( Q \) is the heat added (in joules),
- \( m \) is the mass (in grams),
- \( c \) is the specific heat capacity (in J/g°C),
- \( \Delta T \) is the change in temperature (in °C).
Given:
- Specific heat of water \( c_{water} = 4.18 \, \text{J/(g°C)} \)
- Specific heat of wood \( c_{wood} = 1.97 \, \text{J/(g°C)} \)
### Analysis of Each Statement:
1. **Regardless of mass, wood will heat up less than water if the same heat is added.**
This statement is misleading. The temperature change depends on the specific heat capacity and mass. If you add heat to both substances, they won’t necessarily have a consistent relationship without knowing the mass.
2. **Given equal masses, wood will heat up less than water if the same heat is added.**
This statement is **incorrect**. Since wood has a lower specific heat capacity than water, for equal masses, wood will experience a greater temperature change compared to water when the same amount of heat is added. Therefore, water will heat up less (have a smaller temperature increase) than wood under these conditions.
3. **Given equal masses, water will heat up less than wood if the same heat is added.**
This statement is **correct**, because with equal masses, the higher specific heat of water means it will experience a smaller temperature increase compared to wood when the same amount of heat is added.
4. **Regardless of mass, water will heat up less than wood if the same heat is added.**
This statement is also misleading because, without specifying mass, one cannot directly compare the temperature changes of water and wood. The relative heat-up will depend on the mass as well as the specific heat capacities.
### Conclusion:
The correct statement is:
**Given equal masses, water will heat up less than wood if the same heat is added.**
\[ Q = mc\Delta T \]
where:
- \( Q \) is the heat added (in joules),
- \( m \) is the mass (in grams),
- \( c \) is the specific heat capacity (in J/g°C),
- \( \Delta T \) is the change in temperature (in °C).
Given:
- Specific heat of water \( c_{water} = 4.18 \, \text{J/(g°C)} \)
- Specific heat of wood \( c_{wood} = 1.97 \, \text{J/(g°C)} \)
### Analysis of Each Statement:
1. **Regardless of mass, wood will heat up less than water if the same heat is added.**
This statement is misleading. The temperature change depends on the specific heat capacity and mass. If you add heat to both substances, they won’t necessarily have a consistent relationship without knowing the mass.
2. **Given equal masses, wood will heat up less than water if the same heat is added.**
This statement is **incorrect**. Since wood has a lower specific heat capacity than water, for equal masses, wood will experience a greater temperature change compared to water when the same amount of heat is added. Therefore, water will heat up less (have a smaller temperature increase) than wood under these conditions.
3. **Given equal masses, water will heat up less than wood if the same heat is added.**
This statement is **correct**, because with equal masses, the higher specific heat of water means it will experience a smaller temperature increase compared to wood when the same amount of heat is added.
4. **Regardless of mass, water will heat up less than wood if the same heat is added.**
This statement is also misleading because, without specifying mass, one cannot directly compare the temperature changes of water and wood. The relative heat-up will depend on the mass as well as the specific heat capacities.
### Conclusion:
The correct statement is:
**Given equal masses, water will heat up less than wood if the same heat is added.**