What is the heat needed to raise the temperature of 24.7-kg silver from 14.0 degrees Celsius to 30.0 degrees Celsius? Specific heat capacity of silver is 236 J/(kg°C).

5.93 E4 J
8.18 E4 J
9.32 E4 J
1.16 E5 J

To calculate the heat needed 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 of the substance (in kilograms, kg)
- \( c \) is the specific heat capacity (in joules per kilogram per degree Celsius, J/(kg°C))
- \( \Delta T \) is the change in temperature (in degrees Celsius, °C)

Given:
- \( m = 24.7 \) kg
- \( c = 236 \) J/(kg°C)
- Initial temperature (\( T_i \)) = 14.0°C
- Final temperature (\( T_f \)) = 30.0°C

First, calculate the change in temperature (\( \Delta T \)):

\[ \Delta T = T_f - T_i = 30.0°C - 14.0°C = 16.0°C \]

Now, use the formula to find \( Q \):

\[ Q = mc\Delta T \]
\[ Q = (24.7 \, \text{kg}) \times (236 \, \text{J/(kg°C)}) \times (16.0 \, \text{°C}) \]

\[ Q = 24.7 \times 236 \times 16 \]

Perform the multiplication:

\[ Q = 24.7 \times 236 = 5829.2 \]
\[ Q = 5829.2 \times 16 = 93267.2 \, \text{J} \]

The heat needed is:

\[ Q \approx 9.33 \times 10^4 \, \text{J} \]

Therefore, the closest option is:

\[ \boxed{9.32 \times 10^4 \, \text{J}} \]

Would you like more details or have any questions? Here are some related questions for further exploration:

1. What is the specific heat capacity?
2. How do you convert from Celsius to Kelvin?
3. What is the formula for heat energy involving phase changes?
4. How does specific heat capacity vary between different substances?
5. What are the units of specific heat capacity in the SI system?
6. How do you measure the temperature change in a laboratory setting?
7. Can specific heat capacity change with temperature?
8. What is the significance of the specific heat capacity in thermal energy calculations?

**Tip:** When dealing with heat energy problems, always keep track of your units and make sure they are consistent throughout the calculation.

Learn how to calculate the heat energy needed to raise the temperature of a 24.7-kg silver from 14.0°C to 30.0°C using the specific heat capacity of silver (236 J/(kg°C)). Detailed step-by-step solution provided.

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