hat is the heat needed to raise the temperature of 23.6-kg silver from 16.0 degrees Celsius to 38.0 degrees Celsius? Specific heat capacity of silver is 236 J/(kg°C).

8.91 E4 J
1.23 E5 J
2.11 E5 J
3.01 E5 J

To determine the heat required to raise the temperature of a substance, we use the formula:

\[ Q = mc\Delta T \]

where:
- \( Q \) is the heat energy (in joules, J)
- \( m \) is the mass (in kilograms, kg)
- \( c \) is the specific heat capacity (in J/(kg°C))
- \( \Delta T \) is the change in temperature (in °C)

Given:
- Mass \( m = 23.6 \, \text{kg} \)
- Specific heat capacity \( c = 236 \, \text{J/(kg°C)} \)
- Initial temperature \( T_{\text{initial}} = 16.0 \, \text{°C} \)
- Final temperature \( T_{\text{final}} = 38.0 \, \text{°C} \)

First, calculate the change in temperature (\( \Delta T \)):
\[ \Delta T = T_{\text{final}} - T_{\text{initial}} = 38.0 \, \text{°C} - 16.0 \, \text{°C} = 22.0 \, \text{°C} \]

Next, substitute the values into the heat formula:
\[ Q = mc\Delta T = 23.6 \, \text{kg} \times 236 \, \text{J/(kg°C)} \times 22.0 \, \text{°C} \]

Calculate the heat energy:
\[ Q = 23.6 \times 236 \times 22.0 \]
\[ Q = 123,123.2 \, \text{J} \]

So, the heat needed is approximately:
\[ Q \approx 1.23 \times 10^5 \, \text{J} \]

Therefore, the correct answer is:
\[ 1.23 \times 10^5 \, \text{J} \]

Would you like further details or have any questions?

Here are 8 related questions:

1. What is the specific heat capacity of a substance and how is it determined?
2. How do different materials affect the amount of heat required to change their temperature?
3. Can you explain the concept of thermal equilibrium?
4. What is the significance of the heat capacity in real-world applications?
5. How does the mass of an object influence the heat required for temperature change?
6. What are some practical examples of using the specific heat capacity in everyday life?
7. How would the heat required change if the initial temperature were lower?
8. How is the heat energy calculated in a phase change (e.g., melting or boiling)?

**Tip:** Always ensure units are consistent when performing calculations to avoid errors.

Learn how to calculate the heat energy required to raise the temperature of 23.6-kg silver from 16.0°C to 38.0°C using the specific heat capacity of silver. Follow the detailed step-by-step solution and understand the formula Q = mcΔT. Suitable for high school students studying thermodynamics.

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