What is the heat required to raise the temperature of a 1.5 kg mass by 120°C if the specific heat of the mass is 0.37cal / (g deg) * C

Solution

Q=1.5x1000 gx0.37 cal/g°C ×120°C = 66600 cal

As always, care must be taken in selecting the correct units. Negative answers indicate extraction of heat or heat loss.

Heat conduction through a material is derived from the following relationship

To calculate the heat required to raise the temperature of a mass, we use the formula for heat transfer:

\[
Q = mc\Delta T
\]

Where:
- \(Q\) is the heat energy (in calories),
- \(m\) is the mass of the object (in grams),
- \(c\) is the specific heat capacity of the material (in \(\text{cal/g°C}\)),
- \(\Delta T\) is the change in temperature (in °C).

### Given:
- Mass (\(m\)) = \(1.5 \, \text{kg} = 1.5 \times 1000 \, \text{g} = 1500 \, \text{g}\),
- Specific heat capacity (\(c\)) = \(0.37 \, \text{cal/g°C}\),
- Temperature change (\(\Delta T\)) = \(120 \, \text{°C}\).

### Calculation:

\[
Q = 1500 \, \text{g} \times 0.37 \, \text{cal/g°C} \times 120 \, \text{°C}
\]

Now let's compute:

\[
Q = 66600 \, \text{cal}
\]

### Conclusion:
The heat required to raise the temperature of the 1.5 kg mass by 120°C is **66,600 calories**.

### Explanation of Units:
- Mass was converted from kilograms to grams to match the unit of specific heat capacity (\(\text{cal/g°C}\)).
- The formula provided is specific for heat conduction, and the positive result means heat is being absorbed by the material.

Would you like more details on the heat conduction formula or any specific area?

### Further Questions:
1. How does the specific heat capacity affect the amount of heat required?
2. What would happen if the mass were doubled while keeping the same specific heat capacity?
3. How would the result change if the temperature increase were 100°C instead of 120°C?
4. What is the difference between heat and temperature in thermodynamic terms?
5. Can you explain how heat conduction differs from convection and radiation?

### Tip:
Always ensure that the units of mass and specific heat capacity match to avoid calculation errors.

What is the heat required to raise the temperature of a 1.5 kg mass by 120°C if the specific heat of the mass is 0.37 cal/g°C?

Learn how to calculate the heat required to raise the temperature of a 1.5 kg mass by 120°C, using the heat transfer formula Q = mcΔT. This problem includes key concepts from thermodynamics and unit conversion. Suitable for students in Grades 9-12.

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