To determine the amount of heat needed to change solid gold to liquid gold at its melting point, we use the concept of latent heat of fusion. The latent heat of fusion is the amount of energy required to change a substance from the solid phase to the liquid phase at constant temperature.
Here's the step-by-step solution:
1. Identify the given values:
- Mass of gold ([tex]\( m \)[/tex]): 5.42 grams
- Latent heat of fusion of gold ([tex]\( L \)[/tex]): 66.6 J/g
2. Use the formula to calculate the heat needed ([tex]\( Q \)[/tex]):
[tex]\[ Q = m \times L \][/tex]
3. Substitute the given values into the formula:
[tex]\[ Q = 5.42 \text{ grams} \times 66.6 \text{ J/g} \][/tex]
4. Perform the multiplication:
[tex]\[ Q = 5.42 \times 66.6 = 360.972 \text{ joules} \][/tex]
5. Round the result to the nearest whole number (if applicable):
[tex]\[ Q \approx 361 \text{ joules} \][/tex]
Therefore, the heat needed to change 5.42 grams of solid gold to liquid gold at its melting point is approximately 361 joules.
So, the correct answer is:
- 361 joules
