Answer :
To solve the problem, we need to determine the final temperature of the water after it loses a certain amount of heat. Let's go through the steps:
1. Understand the Problem:
We have a 0.250 kg sample of water initially at a temperature of 99 °C. This water loses 7500 Joules of heat. We aim to find its final temperature after losing this heat.
2. Relevant Formula:
To find the change in temperature when heat is lost or gained, we can use the formula:
[tex]\[
\Delta T = \frac{Q}{m \times c}
\][/tex]
where:
- [tex]\(\Delta T\)[/tex] is the change in temperature,
- [tex]\(Q\)[/tex] is the heat lost or gained (in Joules),
- [tex]\(m\)[/tex] is the mass (in kg),
- [tex]\(c\)[/tex] is the specific heat capacity. For water, [tex]\(c = 4181 \, \text{J/(kg°C)}\)[/tex].
3. Plug in the Values:
- The mass of the water, [tex]\(m = 0.250 \, \text{kg}\)[/tex],
- The heat lost, [tex]\(Q = 7500 \, \text{J}\)[/tex],
- The specific heat capacity of water, [tex]\(c = 4181 \, \text{J/(kg°C)}\)[/tex].
Using the formula, calculate [tex]\(\Delta T\)[/tex]:
[tex]\[
\Delta T = \frac{7500}{0.250 \times 4181} \approx 7.18 \, \text{°C}
\][/tex]
4. Calculate the Final Temperature:
Since the water is losing heat, its temperature decreases. Therefore, the final temperature ([tex]\(T_{\text{final}}\)[/tex]) can be calculated by subtracting the temperature change ([tex]\(\Delta T\)[/tex]) from the initial temperature ([tex]\(T_{\text{initial}}\)[/tex]):
[tex]\[
T_{\text{final}} = T_{\text{initial}} - \Delta T = 99 \, \text{°C} - 7.18 \, \text{°C} \approx 91.82 \, \text{°C}
\][/tex]
5. Determine the Closest Answer:
The calculated final temperature is approximately 91.82 °C. The closest answer choice is 92 degrees.
Therefore, the best choice that represents the solution is 92 degrees.
1. Understand the Problem:
We have a 0.250 kg sample of water initially at a temperature of 99 °C. This water loses 7500 Joules of heat. We aim to find its final temperature after losing this heat.
2. Relevant Formula:
To find the change in temperature when heat is lost or gained, we can use the formula:
[tex]\[
\Delta T = \frac{Q}{m \times c}
\][/tex]
where:
- [tex]\(\Delta T\)[/tex] is the change in temperature,
- [tex]\(Q\)[/tex] is the heat lost or gained (in Joules),
- [tex]\(m\)[/tex] is the mass (in kg),
- [tex]\(c\)[/tex] is the specific heat capacity. For water, [tex]\(c = 4181 \, \text{J/(kg°C)}\)[/tex].
3. Plug in the Values:
- The mass of the water, [tex]\(m = 0.250 \, \text{kg}\)[/tex],
- The heat lost, [tex]\(Q = 7500 \, \text{J}\)[/tex],
- The specific heat capacity of water, [tex]\(c = 4181 \, \text{J/(kg°C)}\)[/tex].
Using the formula, calculate [tex]\(\Delta T\)[/tex]:
[tex]\[
\Delta T = \frac{7500}{0.250 \times 4181} \approx 7.18 \, \text{°C}
\][/tex]
4. Calculate the Final Temperature:
Since the water is losing heat, its temperature decreases. Therefore, the final temperature ([tex]\(T_{\text{final}}\)[/tex]) can be calculated by subtracting the temperature change ([tex]\(\Delta T\)[/tex]) from the initial temperature ([tex]\(T_{\text{initial}}\)[/tex]):
[tex]\[
T_{\text{final}} = T_{\text{initial}} - \Delta T = 99 \, \text{°C} - 7.18 \, \text{°C} \approx 91.82 \, \text{°C}
\][/tex]
5. Determine the Closest Answer:
The calculated final temperature is approximately 91.82 °C. The closest answer choice is 92 degrees.
Therefore, the best choice that represents the solution is 92 degrees.
