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$[/tex\] Of Heat Is Applied? Use $q = M C_p \Delta T$.A.

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Introduction

In the realm of thermodynamics, specific heat is a crucial property that determines the amount of heat energy required to raise the temperature of a substance by a given amount. It is an essential concept in chemistry, physics, and engineering, as it helps us understand the thermal behavior of various materials. In this article, we will delve into the specific heat of a substance and explore how to calculate it using the given formula: $q = m C_p \Delta T$.

What is Specific Heat?

Specific heat, denoted by the symbol $C_p$, 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. The specific heat of a substance depends on its chemical composition, molecular structure, and physical state (solid, liquid, or gas).

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

The formula $q = m C_p \Delta T$ is a fundamental equation in thermodynamics that relates the heat energy transferred to a substance to its mass, specific heat, and temperature change. Here's a breakdown of the variables:

  • q$: the amount of heat energy transferred to the substance (in joules, J)

  • m$: the mass of the substance (in kilograms, kg)

  • C_p$: the specific heat of the substance (in joules per kilogram per degree Celsius, J/kgΒ°C)

  • \Delta T$: the change in temperature (in degrees Celsius, Β°C)

Calculating Specific Heat

Now that we have the formula, let's apply it to the given problem. We are told 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 need to find the specific heat of the substance.

First, we need to calculate the change in temperature ($\Delta T$):

Ξ”T=Tfβˆ’Ti=70.0∘Cβˆ’10.0∘C=60.0∘C\Delta T = T_f - T_i = 70.0^{\circ} C - 10.0^{\circ} C = 60.0^{\circ} C

Next, we can plug in the values into the formula:

q=mCpΞ”Tq = m C_p \Delta T

2,520J=(10.0kg)(Cp)(60.0∘C)2,520 J = (10.0 kg) (C_p) (60.0^{\circ} C)

To solve for $C_p$, we can rearrange the formula:

Cp=qmΞ”TC_p = \frac{q}{m \Delta T}

Cp=2,520J(10.0kg)(60.0∘C)C_p = \frac{2,520 J}{(10.0 kg) (60.0^{\circ} C)}

Cp=2,520J600kg∘CC_p = \frac{2,520 J}{600 kg^{\circ} C}

Cp=4.2J/kg∘CC_p = 4.2 J/kg^{\circ} C

Therefore, the specific heat of the substance is $4.2 J/kg^{\circ} C$.

Conclusion

In conclusion, specific heat is a fundamental property of a substance that determines its ability to absorb and release heat energy. The formula $q = m C_p \Delta T$ is a powerful tool for calculating specific heat, and we have applied it to a given problem to find the specific heat of a substance. By understanding specific heat, we can better comprehend the thermal behavior of various materials and make informed decisions in fields such as chemistry, physics, and engineering.

Applications of Specific Heat

Specific heat has numerous applications in various fields, including:

  • Thermal energy storage: Specific heat is used to design thermal energy storage systems, which can store heat energy for later use.
  • Heat transfer: Specific heat is used to calculate heat transfer rates in various systems, such as heat exchangers and radiators.
  • Materials science: Specific heat is used to study the thermal properties of materials and design new materials with specific thermal properties.
  • Chemical engineering: Specific heat is used to design and optimize chemical processes, such as distillation and reaction systems.

Limitations of Specific Heat

While specific heat is a useful property, it has some limitations. For example:

  • Temperature dependence: Specific heat can vary with temperature, which can affect its accuracy.
  • Pressure dependence: Specific heat can also vary with pressure, which can affect its accuracy.
  • Material properties: Specific heat can be affected by the material's properties, such as its molecular structure and chemical composition.

Future Research Directions

Future research directions in specific heat include:

  • Developing new materials: Researchers are working on developing new materials with specific thermal properties, such as high specific heat capacity materials.
  • Improving measurement techniques: Researchers are working on improving measurement techniques to accurately measure specific heat.
  • Applications in energy storage: Researchers are exploring the use of specific heat in thermal energy storage systems.

Conclusion

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: $q = m C_p \Delta T$, where $q$ is the amount of heat energy transferred, $m$ is the mass of the substance, $C_p$ is the specific heat of the substance, and $\Delta T$ is the change in temperature.

Q: What are some common applications of specific heat?

A: Specific heat has numerous applications in various fields, including:

  • Thermal energy storage: Specific heat is used to design thermal energy storage systems, which can store heat energy for later use.
  • Heat transfer: Specific heat is used to calculate heat transfer rates in various systems, such as heat exchangers and radiators.
  • Materials science: Specific heat is used to study the thermal properties of materials and design new materials with specific thermal properties.
  • Chemical engineering: Specific heat is used to design and optimize chemical processes, such as distillation and reaction systems.

Q: What are some limitations of specific heat?

A: While specific heat is a useful property, it has some limitations, including:

  • Temperature dependence: Specific heat can vary with temperature, which can affect its accuracy.
  • Pressure dependence: Specific heat can also vary with pressure, which can affect its accuracy.
  • Material properties: Specific heat can be affected by the material's properties, such as its molecular structure and chemical composition.

Q: How can I measure specific heat?

A: Specific heat can be measured using various techniques, including:

  • Calorimetry: This involves measuring the heat energy transferred to a substance as it is heated or cooled.
  • Thermal analysis: This involves measuring the thermal properties of a substance, such as its specific heat capacity, thermal conductivity, and thermal diffusivity.

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 incorrect units: Make sure to use the correct units for specific heat, such as joules per kilogram per degree Celsius (J/kgΒ°C).
  • Failing to account for temperature dependence: Specific heat can vary with temperature, so make sure to account for this when calculating specific heat.
  • Ignoring material properties: Specific heat can be affected by the material's properties, such as its molecular structure and chemical composition.

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

A: Some future research directions in specific heat include:

  • Developing new materials: Researchers are working on developing new materials with specific thermal properties, such as high specific heat capacity materials.
  • Improving measurement techniques: Researchers are working on improving measurement techniques to accurately measure specific heat.
  • Applications in energy storage: Researchers are exploring the use of specific heat in thermal energy storage systems.

Q: How can I apply specific heat in my work or research?

A: Specific heat can be applied in a variety of fields, including:

  • Thermal energy storage: Use specific heat to design thermal energy storage systems that can store heat energy for later use.
  • Heat transfer: Use specific heat to calculate heat transfer rates in various systems, such as heat exchangers and radiators.
  • Materials science: Use specific heat to study the thermal properties of materials and design new materials with specific thermal properties.
  • Chemical engineering: Use specific heat to design and optimize chemical processes, such as distillation and reaction systems.

Conclusion

In conclusion, specific heat is a fundamental property of a substance that determines its ability to absorb and release heat energy. By understanding specific heat, we can better comprehend the thermal behavior of various materials and make informed decisions in fields such as chemistry, physics, and engineering.