Assuming All The Substances Below Have The Same Mass, Which Substance Requires The Least Energy To Raise Its Temperature By $7^{\circ} C$? Use The Table To Help You Answer The Question.$\[ \begin{tabular}{|c|c|} \hline \text{Substance} &

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Understanding the Problem

When dealing with the concept of energy and temperature, it's essential to consider the specific heat capacity of a substance. The specific heat capacity is the amount of heat energy required to raise the temperature of a unit mass of a substance by one degree Celsius (or Kelvin). In this problem, we are given a table with various substances and their specific heat capacities. We need to determine which substance requires the least energy to raise its temperature by $7^{\circ} C$.

The Role of Specific Heat Capacity

The specific heat capacity of a substance is a measure of its ability to absorb and release heat energy. Substances with high specific heat capacities can absorb and release more heat energy without a significant change in temperature. On the other hand, substances with low specific heat capacities require less heat energy to produce the same change in temperature.

Analyzing the Table

Substance	Specific Heat Capacity (J/g°C)
Water	4.184
Copper	0.385
Aluminum	0.904
Iron	0.449
Silver	0.235

Determining the Substance with the Least Energy Requirement

To determine which substance requires the least energy to raise its temperature by $7^{\circ} C$, we need to consider the specific heat capacity of each substance. The substance with the lowest specific heat capacity will require the least energy to produce the same change in temperature.

Calculating the Energy Requirement

The energy required to raise the temperature of a substance by $7^{\circ} C$ can be calculated using the formula:

Energy (J) = Specific Heat Capacity (J/g°C) x Mass (g) x Temperature Change (°C)

Since we are assuming all the substances have the same mass, we can ignore the mass term in the formula. Therefore, the energy required to raise the temperature of each substance by $7^{\circ} C$ is directly proportional to its specific heat capacity.

Comparing the Energy Requirements

Based on the table, we can see that Silver has the lowest specific heat capacity of 0.235 J/g°C. Therefore, it will require the least energy to raise its temperature by $7^{\circ} C$.

Conclusion

In conclusion, when all the substances have the same mass, the substance that requires the least energy to raise its temperature by $7^{\circ} C$ is Silver. This is because Silver has the lowest specific heat capacity among the given substances, indicating that it can absorb and release heat energy more efficiently.

Implications and Applications

The concept of specific heat capacity has significant implications in various fields, including engineering, physics, and chemistry. Understanding the specific heat capacity of a substance can help us design more efficient systems for heating and cooling, as well as predict the behavior of materials under different temperature conditions.

Real-World Examples

In real-world applications, the concept of specific heat capacity is crucial in designing systems for temperature control. For instance, in the production of steel, the specific heat capacity of the material is taken into account to determine the optimal temperature for rolling and shaping. Similarly, in the design of refrigeration systems, the specific heat capacity of the refrigerant is critical in determining the efficiency of the system.

Limitations and Future Directions

While the concept of specific heat capacity is well-established, there are still limitations and areas for future research. For instance, the specific heat capacity of a substance can vary depending on its crystal structure, impurities, and other factors. Therefore, further research is needed to develop more accurate models for predicting the specific heat capacity of materials under different conditions.

Conclusion

In conclusion, the substance that requires the least energy to raise its temperature by $7^{\circ} C$ is Silver. This is due to its low specific heat capacity, which indicates that it can absorb and release heat energy more efficiently. The concept of specific heat capacity has significant implications in various fields and is crucial in designing systems for temperature control. Further research is needed to develop more accurate models for predicting the specific heat capacity of materials under different conditions.

Q: What is specific heat capacity?

A: Specific heat capacity is the amount of heat energy required to raise the temperature of a unit mass of a substance by one degree Celsius (or Kelvin). It is a measure of a substance's ability to absorb and release heat energy.

Q: Why is specific heat capacity important?

A: Specific heat capacity is important because it helps us understand how a substance will behave under different temperature conditions. It is crucial in designing systems for temperature control, such as heating and cooling systems, and in predicting the behavior of materials under different temperature conditions.

Q: How is specific heat capacity measured?

A: Specific heat capacity is typically measured using a calorimeter, which is a device that measures the amount of heat energy required to raise the temperature of a substance. The measurement is usually performed at a constant pressure and temperature.

Q: What are some common applications of specific heat capacity?

A: Specific heat capacity has many applications in various fields, including:

• Engineering: Specific heat capacity is used to design heating and cooling systems, as well as to predict the behavior of materials under different temperature conditions.
• Physics: Specific heat capacity is used to study the behavior of materials under different temperature conditions, and to understand the thermodynamic properties of substances.
• Chemistry: Specific heat capacity is used to study the thermodynamic properties of substances, and to predict the behavior of materials under different temperature conditions.
• Materials Science: Specific heat capacity is used to study the thermodynamic properties of materials, and to predict the behavior of materials under different temperature conditions.

Q: What are some common substances with high specific heat capacities?

A: Some common substances with high specific heat capacities include:

• Water: Water has a specific heat capacity of 4.184 J/g°C, which is one of the highest among all substances.
• Ceramics: Ceramics have high specific heat capacities due to their complex crystal structures.
• Metals: Some metals, such as copper and aluminum, have high specific heat capacities due to their high atomic masses and complex crystal structures.

Q: What are some common substances with low specific heat capacities?

A: Some common substances with low specific heat capacities include:

• Gases: Gases, such as helium and hydrogen, have low specific heat capacities due to their low atomic masses and simple molecular structures.
• Liquids: Some liquids, such as mercury and bromine, have low specific heat capacities due to their low atomic masses and simple molecular structures.
• Solids: Some solids, such as graphite and diamond, have low specific heat capacities due to their simple crystal structures and low atomic masses.

Q: How does temperature affect specific heat capacity?

A: Temperature can affect specific heat capacity in several ways:

• Temperature dependence: The specific heat capacity of a substance can vary with temperature due to changes in its crystal structure or molecular interactions.
• Phase transitions: Specific heat capacity can change significantly during phase transitions, such as melting or boiling.
• Thermal expansion: Specific heat capacity can change with thermal expansion, which can affect the material's density and specific heat capacity.

Q: Can specific heat capacity be affected by external factors?

A: Yes, specific heat capacity can be affected by external factors, such as:

• Pressure: Pressure can affect the specific heat capacity of a substance by changing its crystal structure or molecular interactions.
• Concentration: Concentration can affect the specific heat capacity of a substance by changing its molecular interactions or crystal structure.
• Impurities: Impurities can affect the specific heat capacity of a substance by changing its crystal structure or molecular interactions.

Q: How can specific heat capacity be used in real-world applications?

A: Specific heat capacity can be used in various real-world applications, such as:

• Heating and cooling systems: Specific heat capacity can be used to design efficient heating and cooling systems.
• Materials selection: Specific heat capacity can be used to select materials for specific applications, such as high-temperature applications or cryogenic applications.
• Thermal energy storage: Specific heat capacity can be used to design thermal energy storage systems, which can store thermal energy for later use.

Q: What are some common mistakes to avoid when working with specific heat capacity?

A: Some common mistakes to avoid when working with specific heat capacity include:

• Ignoring temperature dependence: Failing to account for temperature dependence can lead to inaccurate results.
• Ignoring phase transitions: Failing to account for phase transitions can lead to inaccurate results.
• Ignoring external factors: Failing to account for external factors, such as pressure or concentration, can lead to inaccurate results.