A 10-gram Aluminum Cube Absorbs 677 Joules When Its Temperature Is Increased From $50^{\circ} C$ To $125^{\circ} C$. What Is The Specific Heat Of Aluminum? Express The Answer To The Hundredths Place.

Introduction

The specific heat of a substance is a measure of the amount of heat energy required to raise the temperature of a unit mass of the substance by one degree Celsius. In this problem, we are given a 10-gram aluminum cube that absorbs 677 joules when its temperature is increased from $50^{\circ} C$ to $125^{\circ} C$. We need to find the specific heat of aluminum.

The Formula for Specific Heat

The formula for specific heat is given by:

$$c = \frac{Q}{m \Delta T}$$

where:

• c$ is the specific heat capacity of the substance

• Q$ is the amount of heat energy absorbed by the substance

• m$ is the mass of the substance

• \Delta T$ is the change in temperature

Given Values

We are given the following values:

• Q = 677$ joules

• m = 10$ grams

• $$\Delta T = 125^{\circ} C - 50^{\circ} C = 75^{\circ} C$$

Calculating Specific Heat

Now, we can plug in the given values into the formula for specific heat:

$$c = \frac{677}{10 \times 75}$$

$$c = \frac{677}{750}$$

$$c = 0.9033$$

Rounding to the Hundredths Place

We are asked to express the answer to the hundredths place. Therefore, we round the value of $c$ to the hundredths place:

$$c = 0.90$$

Conclusion

In this problem, we found the specific heat of aluminum by using the formula for specific heat and plugging in the given values. We calculated that the specific heat of aluminum is $0.90$ joules per gram per degree Celsius.

Importance of Specific Heat

The specific heat of a substance is an important property that is used in many applications, such as:

• Thermal energy storage: Specific heat is used to determine the amount of heat energy that can be stored in a substance.
• Heat transfer: Specific heat is used to determine the rate of heat transfer between two substances.
• Materials science: Specific heat is used to determine the thermal properties of materials.

Real-World Applications

The specific heat of aluminum is used in many real-world applications, such as:

• Heat exchangers: Aluminum is used in heat exchangers due to its high specific heat capacity.
• Thermal energy storage systems: Aluminum is used in thermal energy storage systems due to its high specific heat capacity.
• Aerospace engineering: Aluminum is used in aerospace engineering due to its high specific heat capacity and low density.

Limitations of the Problem

This problem assumes that the specific heat capacity of aluminum is constant over the temperature range of $50^{\circ} C$ to $125^{\circ} C$. However, in reality, the specific heat capacity of aluminum may vary over this temperature range.

Future Research Directions

Future research directions in this area may include:

• Measuring the specific heat capacity of aluminum over a wider temperature range
• Investigating the effects of impurities on the specific heat capacity of aluminum
• Developing new materials with high specific heat capacities

Conclusion

In conclusion, we found the specific heat of aluminum by using the formula for specific heat and plugging in the given values. We calculated that the specific heat of aluminum is $0.90$ joules per gram per degree Celsius. This value is important for many applications, including thermal energy storage, heat transfer, and materials science.

Q&A: Specific Heat of Aluminum

Q: What is the specific heat of aluminum?

A: The specific heat of aluminum is 0.90 joules per gram per degree Celsius.

Q: What is the formula for specific heat?

A: The formula for specific heat is given by:

$$c = \frac{Q}{m \Delta T}$$

where:

• c$ is the specific heat capacity of the substance

• Q$ is the amount of heat energy absorbed by the substance

• m$ is the mass of the substance

• \Delta T$ is the change in temperature

Q: What are the given values in this problem?

A: The given values are:

• Q = 677$ joules

• m = 10$ grams

• $$\Delta T = 125^{\circ} C - 50^{\circ} C = 75^{\circ} C$$

Q: How do you calculate the specific heat of aluminum?

A: To calculate the specific heat of aluminum, you plug in the given values into the formula for specific heat:

$$c = \frac{677}{10 \times 75}$$

$$c = \frac{677}{750}$$

$$c = 0.9033$$

Q: Why is specific heat important?

A: Specific heat is an important property that is used in many applications, such as:

• Thermal energy storage: Specific heat is used to determine the amount of heat energy that can be stored in a substance.
• Heat transfer: Specific heat is used to determine the rate of heat transfer between two substances.
• Materials science: Specific heat is used to determine the thermal properties of materials.

Q: What are some real-world applications of the specific heat of aluminum?

A: The specific heat of aluminum is used in many real-world applications, such as:

• Heat exchangers: Aluminum is used in heat exchangers due to its high specific heat capacity.
• Thermal energy storage systems: Aluminum is used in thermal energy storage systems due to its high specific heat capacity.
• Aerospace engineering: Aluminum is used in aerospace engineering due to its high specific heat capacity and low density.

Q: What are some limitations of this problem?

A: This problem assumes that the specific heat capacity of aluminum is constant over the temperature range of $50^{\circ} C$ to $125^{\circ} C$. However, in reality, the specific heat capacity of aluminum may vary over this temperature range.

Q: What are some future research directions in this area?

A: Future research directions in this area may include:

• Measuring the specific heat capacity of aluminum over a wider temperature range
• Investigating the effects of impurities on the specific heat capacity of aluminum
• Developing new materials with high specific heat capacities

Q: Why is it important to express the answer to the hundredths place?

A: It is important to express the answer to the hundredths place because it provides a more accurate representation of the specific heat of aluminum.