What Is The Specific Heat Of A Substance If A Mass Of 10.0 Kg Increases In Temperature From $10.0^{\circ} C$ To $70.0^{\circ} C$ When 2,520 J Of Heat Is Applied?Use \$q = M C_p \Delta T$[/tex\].A. $0.00420 \,

Introduction

In thermodynamics, 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 (or Kelvin). It is an important property that helps us understand how a substance responds to changes in temperature. In this article, we will explore the concept of specific heat and how to calculate it using the formula: $q = m C_p \Delta T$.

What is Specific Heat?

Specific heat 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 denoted by the symbol $C_p$ and is typically measured in units of joules per kilogram per degree Celsius (J/kg°C). The specific heat of a substance depends on its composition, structure, and phase (solid, liquid, or gas).

The Formula: $q = m C_p \Delta T$

The formula $q = m C_p \Delta T$ is used to calculate the specific heat of a substance. Here, $q$ is the amount of heat energy applied to the substance, $m$ is the mass of the substance, $C_p$ is the specific heat capacity of the substance, and $\Delta T$ is the change in temperature.

Calculating Specific Heat

Let's use the given problem to calculate the specific heat of a substance. We are given that a mass of 10.0 kg increases in temperature from $10.0^{\circ} C$ to $70.0^{\circ} C$ when 2,520 J of heat is applied. We can use the formula $q = m C_p \Delta T$ to calculate the specific heat of the substance.

Step 1: Calculate the Change in Temperature

The change in temperature is given by $\Delta T = T_f - T_i$, where $T_f$ is the final temperature and $T_i$ is the initial temperature. In this case, $\Delta T = 70.0^{\circ} C - 10.0^{\circ} C = 60.0^{\circ} C$.

Step 2: Rearrange the Formula to Solve for $C_p$

We can rearrange the formula $q = m C_p \Delta T$ to solve for $C_p$ by dividing both sides by $m \Delta T$. This gives us: $C_p = \frac{q}{m \Delta T}$

Step 3: Plug in the Values

We can now plug in the values given in the problem: $q = 2,520 J$, $m = 10.0 kg$, and $\Delta T = 60.0^{\circ} C$. This gives us: $C_p = \frac{2,520 J}{10.0 kg \times 60.0^{\circ} C}$

Step 4: Calculate the Specific Heat

We can now calculate the specific heat of the substance: $C_p = \frac{2,520 J}{600.0 kg^{\circ} C} = 0.00420 J/kg^{\circ} C$

Conclusion

In this article, we have explored the concept of specific heat and how to calculate it using the formula $q = m C_p \Delta T$. We have used a given problem to calculate the specific heat of a substance and have found that the specific heat of the substance is $0.00420 J/kg^{\circ} C$.

References

• [1] Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of physics. John Wiley & Sons.
• [2] Serway, R. A., & Jewett, J. W. (2018). Physics for scientists and engineers. Cengage Learning.

Discussion

What do you think about the concept of specific heat? How do you think it can be applied in real-world situations? Share your thoughts and ideas in the comments below!

Related Topics

• Thermodynamics
• Heat transfer
• Specific heat capacity
• Heat energy
• Temperature change

Further Reading

• [1] "Thermodynamics" by Wikipedia
• [2] "Heat Transfer" by HyperPhysics
• [3] "Specific Heat Capacity" by ScienceDirect

FAQs

• Q: What is specific heat? A: Specific heat is the amount of heat energy required to raise the temperature of a unit mass of a substance by one degree Celsius (or Kelvin).
• Q: How is specific heat calculated? A: Specific heat is calculated using the formula $q = m C_p \Delta T$.
• Q: What is the unit of specific heat? A: The unit of specific heat is joules per kilogram per degree Celsius (J/kg°C).
  Frequently Asked Questions (FAQs) =====================================

Q: What is specific heat?

A: Specific heat 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 an important property that helps us understand how a substance responds to changes in temperature.

Q: How is specific heat calculated?

A: Specific heat is calculated using the formula: $q = m C_p \Delta T$, where $q$ is the amount of heat energy applied to the substance, $m$ is the mass of the substance, $C_p$ is the specific heat capacity of the substance, and $\Delta T$ is the change in temperature.

Q: What is the unit of specific heat?

A: The unit of specific heat is joules per kilogram per degree Celsius (J/kg°C).

Q: What is the difference between specific heat and heat capacity?

A: Specific heat and heat capacity are related but distinct concepts. Specific heat is the amount of heat energy required to raise the temperature of a unit mass of a substance by one degree Celsius (or Kelvin), while heat capacity is the amount of heat energy required to raise the temperature of a substance by one degree Celsius (or Kelvin).

Q: How does specific heat affect the behavior of a substance?

A: Specific heat affects the behavior of a substance by determining how it responds to changes in temperature. Substances with high specific heat values tend to absorb and release heat energy more slowly, while substances with low specific heat values tend to absorb and release heat energy more quickly.

Q: Can specific heat be measured experimentally?

A: Yes, specific heat can be measured experimentally using a variety of techniques, including calorimetry and thermometry.

Q: What are some common applications of specific heat?

A: Specific heat has a wide range of applications, including:

• Thermal energy storage: Specific heat is used to design thermal energy storage systems that can store heat energy for later use.
• Heat transfer: Specific heat is used to design heat transfer systems that can efficiently transfer heat energy between substances.
• Materials science: Specific heat is used to study the properties of materials and their behavior under different temperature conditions.

Q: Can specific heat be used to predict the behavior of a substance under different temperature conditions?

A: Yes, specific heat can be used to predict the behavior of a substance under different temperature conditions. By knowing the specific heat of a substance, we can predict how it will respond to changes in temperature and how it will behave under different thermal conditions.

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

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

• Using the wrong unit: Make sure to use the correct unit of specific heat (J/kg°C) when working with specific heat values.
• Ignoring the temperature range: Make sure to consider the temperature range over which the specific heat value is valid.
• Not accounting for phase changes: Make sure to account for phase changes (e.g., melting or boiling) when working with specific heat values.

Q: Can specific heat be used to design more efficient thermal systems?

A: Yes, specific heat can be used to design more efficient thermal systems. By understanding the specific heat of a substance, we can design thermal systems that are more efficient and effective.

Q: What are some future directions for research in specific heat?

A: Some future directions for research in specific heat include:

• Developing new materials with high specific heat values: Researchers are working to develop new materials with high specific heat values that can be used in a wide range of applications.
• Improving the accuracy of specific heat measurements: Researchers are working to improve the accuracy of specific heat measurements using advanced techniques such as calorimetry and thermometry.
• Developing new applications for specific heat: Researchers are working to develop new applications for specific heat, including thermal energy storage and heat transfer systems.