Calorimetry - Notes for Quick Revision 📚

Calorimetry is the branch of thermal physics that deals with measuring the heat transfer in physical and chemical processes. This subject is crucial for understanding how energy is exchanged in systems, particularly during changes in temperature and phase transitions.

This article provides detailed notes on calorimetry, covering definitions, principles, equations, and applications.

What is Calorimetry?

Definition: Calorimetry is the study of measuring heat transfer during physical changes (like melting or boiling) or chemical reactions.

Device Used: A calorimeter is used to measure the heat exchange.

Basic Concepts in Calorimetry

1. Heat ($Q$)

Heat is energy transferred between systems due to a temperature difference.

Unit: Joule ($\text{J}$).

Formula:

$$Q=mc\mathrm{\Delta }T$$ Where:

• $Q$: Heat energy.
• $m$: Mass of the substance.
• $c$: Specific heat capacity.
• $\mathrm{\Delta }T$: Change in temperature.

2. Temperature ($T$)

• A measure of the average kinetic energy of particles in a system.
• Units: Celsius ($\degree C$), Kelvin ($K$), or Fahrenheit ($\degree F$).

3. Specific Heat Capacity ($c$)

• The amount of heat required to raise the temperature of 1 kg of a substance by $1^\circ C$.
• Units: $\text{J/kg·K}$.

4. Latent Heat ($L$)

The heat required to change the phase of a substance without changing its temperature.

Formula: $$Q=mL$$ Where:

• $L$: Latent heat.
• $m$: Mass of the substance.

Principle of Calorimetry

Law of Conservation of Energy

Heat lost by the hotter body is equal to the heat gained by the cooler body in an isolated system.

Mathematical Expression: $$Q_{\text{lost}}+Q_{\text{gained}}=0$$

Heat Transfer in Calorimetry

1. For a Single Substance

When a substance changes its temperature: $$Q=mc\mathrm{\Delta }T$$

When a substance undergoes a phase change:

$$Q=mL$$

2. For Mixing Two Substances

If two substances of masses $m_1$ and $m_2$, specific heat capacities $c_1$ and $c_2$, and initial temperatures $T_1$ and $T_2$, are mixed: $$m_1{c}_1(T_{\text{final}}-T_1)+m_2{c}_2(T_{\text{final}}-T_2)=0$$ Where $T_{\text{final}}$ is the final equilibrium temperature.

Types of Calorimetry

1. Simple Calorimetry

• Measures heat changes during temperature changes.
• Used for determining specific heat capacity.

2. Bomb Calorimetry

• Measures heat released or absorbed during chemical reactions (e.g., combustion).
• Highly insulated to minimize heat loss.

3. Differential Scanning Calorimetry (DSC)

• Measures the difference in heat required to increase the temperature of a sample and a reference material.
• Used in material science.

Key Terms in Calorimetry

Thermal Equilibrium:

• A state where no heat transfer occurs between objects in contact.

Heat Capacity ($C$):

• The total amount of heat required to raise the temperature of a system by $1^{\circ }C$.
• Formula: $$C=mc$$

Water Equivalent ($W$):

• The mass of water that would absorb the same amount of heat as the calorimeter.
• Formula: $$W=mc$$

Heat in Phase Changes

1. Latent Heat of Fusion ($L_f$)

• The heat required to convert a solid to a liquid at constant temperature.
• Example: Melting of ice.

2. Latent Heat of Vaporization ($L_v$)

• The heat required to convert a liquid to a gas at constant temperature.
• Example: Boiling of water.

Applications of Calorimetry

Determining Specific Heat:

• Used to measure the specific heat capacities of substances.

Measuring Heat of Combustion:

• Bomb calorimeters determine the energy released during combustion.

Food and Nutrition:

• Calorimetry is used to measure the calorific value of food.

Material Science:

• Differential scanning calorimetry analyzes phase transitions in materials.

Industrial Applications:

• Monitoring heat exchange in chemical processes.

Problem-Solving Steps in Calorimetry

Identify the System:

Define the objects involved in the heat exchange.

Write Energy Balance:

• Use the principle of calorimetry ($Q_{\text{lost}}+Q_{\text{gained}}=0$).

Apply Relevant Formulas:

• Use $Q=mc\mathrm{\Delta }T$ for temperature changes.
• Use $Q=mL$ for phase changes.

Solve for Unknowns:

• Solve equations algebraically to find the desired quantity (e.g., $T_{\text{final}}$).

FAQs About Calorimetry

What is the principle of calorimetry?

The principle of calorimetry is based on the conservation of energy, where heat lost by a hotter body equals heat gained by a cooler body.

How does a bomb calorimeter work?

A bomb calorimeter measures the heat released during combustion reactions in a closed, insulated chamber.

What is the difference between heat and temperature?

• Heat is energy transferred due to a temperature difference.
• Temperature measures the average kinetic energy of particles.

Why is water commonly used in calorimeters?

Water has a high specific heat capacity, making it an ideal medium for absorbing or releasing heat.

Calorimetry is a fundamental tool in thermal physics that helps measure heat transfer during various processes. From determining specific heat to measuring the calorific value of substances, calorimetry finds applications in physics, chemistry, nutrition, and industry. These comprehensive notes provide a solid understanding of the concepts, formulas, and problem-solving techniques in calorimetry.

Explore related topics:

• Thermal Physics
• Heat Transfer
• Thermodynamics