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The problem involves calculating the final temperature of a 91 g sample of gold after 874 joules of heat are applied. Here's the step-by-step approach to solving it:

### Given:
- Mass of gold, \( m = 91 \, \text{g} = 0.091 \, \text{kg} \)
- Initial temperature, \( T_{\text{initial}} = 22^\circ \text{C} \)
- Heat applied, \( Q = 874 \, \text{J} \)
- Specific heat capacity of gold, \( c = 0.128 \, \text{J/g}^\circ \text{C} \)
- We need to find the final temperature, \( T_{\text{final}} \).

### Formula:
The formula for heat transfer is:
\[
Q = mc\Delta T
\]
Where:
- \( Q \) is the heat added,
- \( m \) is the mass,
- \( c \) is the specific heat capacity,
- \( \Delta T \) is the change in temperature (\( T_{\text{final}} - T_{\text{initial}} \)).

Rearranging to solve for \( T_{\text{final}} \):
\[
T_{\text{final}} = T_{\text{initial}} + \frac{Q}{mc}
\]

### Calculation:
1. Convert the mass to grams: \( m = 91 \, \text{g} \).
2. Now substitute the values:
\[
T_{\text{final}} = 22^\circ \text{C} + \frac{874 \, \text{J}}{91 \, \text{g} \times 0.128 \, \text{J/g}^\circ \text{C}}
\]

Let me compute that.The final temperature of the gold after 874 joules of heat are applied is approximately \( 97.03^\circ \text{C} \).

Would you like any more details or have any further questions?

Here are 5 related questions to explore:
1. How would the result change if the mass of the gold were doubled?
2. What happens if less heat is applied, say 500 joules? How would the final temperature change?
3. How would the heat required change if the substance was aluminum instead of gold?
4. What is the significance of specific heat capacity in determining temperature changes?
5. How can we calculate the amount of heat lost when a hot object cools down?

**Tip:** Always double-check the units in thermodynamic problems to avoid confusion between different systems (e.g., grams and kilograms).

A 91-g sample of gold is at an initial temperature of 22°C. If 874 joules of heat are applied to the sample, what is the final temperature of the gold?

Learn how to calculate the final temperature of a 91-g gold sample with an initial temperature of 22°C after applying 874 joules of heat. This thermodynamics problem involves concepts of heat transfer and specific heat capacity. Suitable for high school students.

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