A Sample Of An Unknown Substance Has A Mass Of 0.465 Kg. If It Absorbs 3 , 000.0 J 3,000.0 J 3 , 000.0 J Of Heat While Its Temperature Changes From 50.0 ∘ C 50.0^{\circ} C 50. 0 ∘ C To 100.0 ∘ C 100.0^{\circ} C 100. 0 ∘ C , What Is The Specific Heat Of The Substance? Use The Formula

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Introduction

In the field of chemistry, understanding the properties of substances is crucial for various applications, including thermodynamics and heat transfer. One of the essential properties of a substance is its specific heat capacity, which 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 article, we will explore how to calculate the specific heat of an unknown substance using a given sample and heat energy.

The Problem

A sample of an unknown substance has a mass of 0.465 kg. If it absorbs 3000.0 J of heat while its temperature changes from 50.0°C to 100.0°C, what is the specific heat of the substance?

The Formula

To solve this problem, we will use the formula for specific heat capacity, which is given by:

c = Q / (m * ΔT)

where:

  • c is the specific heat capacity of the substance (in J/kg°C)
  • Q is the amount of heat energy absorbed by the substance (in J)
  • m is the mass of the substance (in kg)
  • ΔT is the change in temperature (in °C)

Step 1: Identify the Given Values

We are given the following values:

  • Mass of the substance (m) = 0.465 kg
  • Amount of heat energy absorbed (Q) = 3000.0 J
  • Initial temperature (T1) = 50.0°C
  • Final temperature (T2) = 100.0°C

Step 2: Calculate the Change in Temperature

To calculate the change in temperature (ΔT), we subtract the initial temperature from the final temperature:

ΔT = T2 - T1 = 100.0°C - 50.0°C = 50.0°C

Step 3: Plug in the Values into the Formula

Now that we have all the values, we can plug them into the formula for specific heat capacity:

c = Q / (m * ΔT) = 3000.0 J / (0.465 kg * 50.0°C) = 3000.0 J / 23.25 kg°C = 129.0 J/kg°C

Conclusion

In this article, we calculated the specific heat capacity of an unknown substance using a given sample and heat energy. We used the formula c = Q / (m * ΔT) and plugged in the given values to find the specific heat capacity. The result is c = 129.0 J/kg°C.

Discussion

The specific heat capacity of a substance is an important property that can be used to predict how it will behave in various situations. For example, in a heat transfer system, the specific heat capacity of the substance can affect the rate of heat transfer. Understanding the specific heat capacity of a substance can also help in designing more efficient systems.

Applications

The specific heat capacity of a substance has many practical applications in various fields, including:

  • Thermodynamics: Understanding the specific heat capacity of a substance is crucial in thermodynamics, as it can affect the efficiency of heat transfer systems.
  • Heat Transfer: The specific heat capacity of a substance can affect the rate of heat transfer in various systems, such as heat exchangers and radiators.
  • Materials Science: The specific heat capacity of a substance can affect its behavior in various situations, such as in thermal shock or in high-temperature applications.

Limitations

While the specific heat capacity of a substance is an important property, there are some limitations to consider:

  • Assumptions: The formula c = Q / (m * ΔT) assumes that the heat energy is absorbed uniformly throughout the substance, which may not always be the case.
  • Temperature Range: The specific heat capacity of a substance can vary depending on the temperature range, so it's essential to consider the temperature range when using this property.

Future Work

In future work, it would be interesting to explore the specific heat capacity of various substances and how it affects their behavior in different situations. Additionally, it would be useful to investigate the limitations of the formula c = Q / (m * ΔT) and how to improve it to make it more accurate.

References

  • CRC Handbook of Chemistry and Physics: This reference provides a comprehensive table of specific heat capacities for various substances.
  • Thermodynamics: This reference provides a detailed explanation of thermodynamics and the importance of specific heat capacity in heat transfer systems.

Conclusion

Introduction

In our previous article, we explored how to calculate the specific heat capacity of an unknown substance using a given sample and heat energy. In this article, we will answer some frequently asked questions (FAQs) related to specific heat capacity and its applications.

Q&A

Q: What is specific heat capacity?

A: Specific heat capacity is a measure of the amount of heat energy required to raise the temperature of a unit mass of a substance by one degree Celsius.

Q: Why is specific heat capacity important?

A: Specific heat capacity is important because it can affect the efficiency of heat transfer systems, such as heat exchangers and radiators. It can also affect the behavior of a substance in various situations, such as in thermal shock or in high-temperature applications.

Q: How is specific heat capacity calculated?

A: Specific heat capacity is calculated using the formula c = Q / (m * ΔT), where c is the specific heat capacity, Q is the amount of heat energy absorbed, m is the mass of the substance, and ΔT is the change in temperature.

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

A: Some common applications of specific heat capacity include:

  • Thermodynamics: Understanding the specific heat capacity of a substance is crucial in thermodynamics, as it can affect the efficiency of heat transfer systems.
  • Heat Transfer: The specific heat capacity of a substance can affect the rate of heat transfer in various systems, such as heat exchangers and radiators.
  • Materials Science: The specific heat capacity of a substance can affect its behavior in various situations, such as in thermal shock or in high-temperature applications.

Q: What are some limitations of specific heat capacity?

A: Some limitations of specific heat capacity include:

  • Assumptions: The formula c = Q / (m * ΔT) assumes that the heat energy is absorbed uniformly throughout the substance, which may not always be the case.
  • Temperature Range: The specific heat capacity of a substance can vary depending on the temperature range, so it's essential to consider the temperature range when using this property.

Q: How can I measure specific heat capacity?

A: Specific heat capacity can be measured using various methods, including:

  • Calorimetry: This method involves measuring the heat energy absorbed by a substance as it changes temperature.
  • Thermal Analysis: This method involves measuring the thermal properties of a substance, such as its specific heat capacity, as it changes temperature.

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

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

  • Incorrect units: Make sure to use the correct units for the variables in the formula, such as joules (J) for heat energy and kilograms (kg) for mass.
  • Incorrect values: Double-check the values of the variables in the formula to ensure that they are accurate.
  • Incorrect assumptions: Be aware of the assumptions made in the formula and ensure that they are valid for the specific situation.

Conclusion

In conclusion, specific heat capacity is an essential property that can be used to predict how a substance will behave in various situations. By understanding the formula c = Q / (m * ΔT) and its limitations, you can calculate the specific heat capacity of an unknown substance. Additionally, by being aware of the common applications and limitations of specific heat capacity, you can use this property to make informed decisions in various fields, such as thermodynamics, heat transfer, and materials science.

References

  • CRC Handbook of Chemistry and Physics: This reference provides a comprehensive table of specific heat capacities for various substances.
  • Thermodynamics: This reference provides a detailed explanation of thermodynamics and the importance of specific heat capacity in heat transfer systems.

Further Reading

  • Specific Heat Capacity: This article provides a detailed explanation of specific heat capacity and its applications.
  • Thermal Properties: This article provides a detailed explanation of thermal properties, including specific heat capacity, and their applications.

Glossary

  • Specific Heat Capacity: A measure of the amount of heat energy required to raise the temperature of a unit mass of a substance by one degree Celsius.
  • Heat Energy: The energy transferred from one body to another due to a temperature difference.
  • Mass: A measure of the amount of matter in an object.
  • Temperature: A measure of the average kinetic energy of the particles in a substance.