Let's solve the problem step-by-step to find the mass of the water that is being heated.
1. Given Data:
- Energy provided (Q) = 2500 joules
- Specific heat capacity of water (c) = 4.186 J/g°C
- Initial temperature (T₁) = 20.0°C
- Final temperature (T₂) = 60.0°C
2. Calculate the Change in Temperature (ΔT):
[tex]\[
\Delta T = T_2 - T_1
\][/tex]
[tex]\[
\Delta T = 60.0^\circ C - 20.0^\circ C = 40.0^\circ C
\][/tex]
3. Rearrange the Heat Transfer Formula to solve for the mass (m):
The heat transfer formula is given by:
[tex]\[
Q = mc\Delta T
\][/tex]
We need to solve for m, so rearrange the formula:
[tex]\[
m = \frac{Q}{c\Delta T}
\][/tex]
4. Substitute the Known Values into the Equation:
[tex]\[
m = \frac{2500 \text{ J}}{4.186 \text{ J/g}^\circ \text{C} \times 40.0^\circ \text{C}}
\][/tex]
5. Calculate the Mass:
[tex]\[
m = \frac{2500}{4.186 \times 40.0}
\][/tex]
[tex]\[
m \approx \frac{2500}{167.44}
\][/tex]
[tex]\[
m \approx 14.93 \text{ grams}
\][/tex]
6. Conclusion:
The mass of the water that is being heated is approximately 14.93 grams.
Given the options, neither 15 g, 40 g, 63 g, nor 80 g are exact matches, but the closest option to our calculated mass is 15 g. So, the most reasonable answer from the given choices is:
15 grams
