How Much Heat Is Required To Raise The Temperature Of 150 G Of Ice (specific Heat $= 2.05 \text{ J/g} \cdot \text{°C}$) From $-30^{\circ} \text{C}$ To $-15^{\circ} \text{C}$?Use: $q = Cm \Delta T$A. 4.61 KJ
Understanding the Problem
To solve this problem, we need to use the formula for heat transfer due to temperature change, which is given by $q = cm \Delta T$. Here, $q$ is the amount of heat required, $c$ is the specific heat capacity of the substance, $m$ is the mass of the substance, and $\Delta T$ is the change in temperature.
Calculating the Change in Temperature
The initial temperature of the ice is $-30^{\circ} \text{C}$, and the final temperature is $-15^{\circ} \text{C}$. To find the change in temperature, we subtract the initial temperature from the final temperature:
Calculating the Heat Required
Now that we have the change in temperature, we can plug in the values into the formula for heat transfer:
We are given that the specific heat capacity of ice is $2.05 \text{ J/g} \cdot \text{°C}$, and the mass of the ice is $150 \text{ g}$. Plugging in these values, we get:
Performing the Calculation
To find the amount of heat required, we need to perform the multiplication:
Converting the Answer to Kiljoules
To express the answer in kiljoules, we divide by $1000$:
However, the answer is given as $4.61 \text{ kJ}$. This suggests that there may be an error in the calculation.
Revisiting the Calculation
Let's revisit the calculation to see where the error may be:
Conclusion
The calculation suggests that the amount of heat required to raise the temperature of $150 \text{ g}$ of ice from $-30^{\circ} \text{C}$ to $-15^{\circ} \text{C}$ is $6.075 \text{ kJ}$. However, the answer is given as $4.61 \text{ kJ}$. This discrepancy suggests that there may be an error in the calculation or in the given answer.
Discussion
The problem requires us to use the formula for heat transfer due to temperature change. We need to calculate the change in temperature and then plug in the values into the formula. However, the calculation suggests that the amount of heat required is $6.075 \text{ kJ}$, which is different from the given answer of $4.61 \text{ kJ}$. This discrepancy suggests that there may be an error in the calculation or in the given answer.
Possible Errors
There may be several possible errors in the calculation or in the given answer. Some possible errors include:
- Rounding errors: The calculation may involve rounding errors, which can lead to discrepancies in the answer.
- Unit errors: The units of the answer may be incorrect, which can lead to discrepancies in the answer.
- Calculation errors: The calculation may involve errors, such as incorrect multiplication or division, which can lead to discrepancies in the answer.
Conclusion
The problem requires us to use the formula for heat transfer due to temperature change. We need to calculate the change in temperature and then plug in the values into the formula. However, the calculation suggests that the amount of heat required is $6.075 \text{ kJ}$, which is different from the given answer of $4.61 \text{ kJ}$. This discrepancy suggests that there may be an error in the calculation or in the given answer.
Final Answer
The final answer is:
Q: What is the formula for heat transfer due to temperature change?
A: The formula for heat transfer due to temperature change is given by $q = cm \Delta T$, where $q$ is the amount of heat required, $c$ is the specific heat capacity of the substance, $m$ is the mass of the substance, and $\Delta T$ is the change in temperature.
Q: How do I calculate the change in temperature?
A: To calculate the change in temperature, you need to subtract the initial temperature from the final temperature. For example, if the initial temperature is $-30^{\circ} \text{C}$ and the final temperature is $-15^{\circ} \text{C}$, the change in temperature is $\Delta T = (-15^{\circ} \text{C}) - (-30^{\circ} \text{C}) = 15^{\circ} \text{C}$.
Q: What is the specific heat capacity of ice?
A: The specific heat capacity of ice is $2.05 \text{ J/g} \cdot \text{°C}$.
Q: How do I calculate the amount of heat required to raise the temperature of a substance?
A: To calculate the amount of heat required, you need to use the formula $q = cm \Delta T$. You need to plug in the values of the specific heat capacity, mass, and change in temperature into the formula.
Q: What is the unit of heat transfer?
A: The unit of heat transfer is joules (J).
Q: How do I convert joules to kilojoules?
A: To convert joules to kilojoules, you need to divide the number of joules by $1000$. For example, if you have $6075 \text J}$, you can convert it to kilojoules by dividing by $1000$}{1000} = 6.075 \text{ kJ}$.
Q: What is the final answer to the problem of raising the temperature of 150 g of ice from $-30^{\circ} \text{C}$ to $-15^{\circ} \text{C}$?
A: The final answer to the problem is $4.61 \text{ kJ}$.
Q: Why is there a discrepancy between the calculated answer and the given answer?
A: There may be several possible errors in the calculation or in the given answer, such as rounding errors, unit errors, or calculation errors.
Q: What are some possible errors that can occur in the calculation?
A: Some possible errors that can occur in the calculation include rounding errors, unit errors, and calculation errors.
Q: How can I avoid errors in the calculation?
A: To avoid errors in the calculation, you need to double-check your work, use the correct units, and perform the calculations carefully.
Q: What is the importance of heat transfer in everyday life?
A: Heat transfer is an important concept in everyday life, as it is involved in many processes such as cooking, heating, and cooling.
Q: How does heat transfer affect the environment?
A: Heat transfer can affect the environment in many ways, such as by causing temperature changes, melting ice, and affecting the climate.
Q: What are some real-world applications of heat transfer?
A: Some real-world applications of heat transfer include refrigeration, air conditioning, and heating systems.
Q: How can I apply the concept of heat transfer to real-world problems?
A: You can apply the concept of heat transfer to real-world problems by using the formula $q = cm \Delta T$ and by considering the specific heat capacity, mass, and change in temperature of the substance involved.