To find the equivalent quantity of heat in Joules, we need to convert the given heat from calories to Joules using the conversion factor.
1. Understand the conversion factor:
One calorie is equivalent to 4.184 Joules.
2. Given data:
Heat released: 24,800 calories.
3. Convert calories to Joules:
To convert the given heat in calories to Joules, multiply the amount of heat in calories by the conversion factor (4.184 Joules/calorie).
Calculation:
[tex]\[
24,800 \, \text{calories} \times 4.184 \, \frac{\text{Joules}}{\text{calorie}} = 103,763.2 \, \text{Joules}
\][/tex]
4. Result:
The quantity of heat equivalent to 24,800 calories is 103,763.2 Joules.
After converting the given heat from calories to Joules, we find that the result is 103,763.2 Joules. Therefore, none of the given options directly match our calculated result. However, it is clear that the exact converted value should be close to 103,763.2 Joules.
Thus, given the options:
- [tex]\(9.64 \times 10^{-5} J\)[/tex]
- [tex]\(8.89 \times 18^4 J\)[/tex]
- [tex]\(2.48 \times 18^4 J\)[/tex]
- [tex]\(2.48 \times 18^4 J\)[/tex]
- [tex]\(8.85 \times 10^4 J\)[/tex]
The closest and logical choice is:
- [tex]\(8.85 \times 10^4\)[/tex] Joules, which is approximately 88,500 Joules.
This shows that the problem text may contain a typographical error or rounding in options provided. The closest correct option is [tex]\( \boxed{8.85 \times 10^4 \, J} \)[/tex].
