Introduction:

Thermodynamics is a vital part of Class 11 Physics that deals with heat, energy, and their transformation. One of the essential concepts in this chapter is Specific Heat Capacity. Understanding this topic helps explain how substances respond to heat and why different materials heat up or cool down at different rates.

What is Specific Heat Capacity?

Specific Heat Capacity (c) is defined as the amount of heat required to raise the temperature of one kilogram of a substance by one degree Celsius (or 1 Kelvin).

Formula: Q = mcΔT

Where:

- Q = heat energy supplied (in joules)

- m = mass of the substance (in kg)

- c = specific heat capacity (in J/kg·K)

- ΔT = change in temperature (in °C or K)

Unit and Dimensions of Specific Heat Capacity:

- SI Unit: Joule per kilogram per Kelvin (J/kg·K)

- CGS Unit: Calorie per gram per degree Celsius (cal/g·°C)

- Dimensions: [L² T⁻² Θ⁻¹]

Types of Heat Capacities:

1. Specific Heat at Constant Volume (Cv)

Heat required to raise the temperature at constant volume. Relevant for gases in rigid containers.

2. Specific Heat at Constant Pressure (Cp)

Heat required to raise the temperature at constant pressure. Higher than Cv due to additional work done during expansion.

Relationship for ideal gases: Cp - Cv = R

Molar Specific Heat Capacity:

The heat capacity of 1 mole of a substance.

Units: J/mol·K

Factors Affecting Specific Heat Capacity:

1. Nature of the Material

Metals have low specific heat, water has high specific heat.

2. Phase of Substance

Solids, liquids, and gases have different specific heats.

3. Temperature Range

Specific heat can vary with temperature.

Applications of Specific Heat Capacity:

- Cooking utensils

- Climate control

- Automobile cooling systems

- Calorimetry

Worked Examples:

Example 1

How much heat is needed to raise the temperature of 2 kg of water from 25°C to 75°C?

Given: c = 4186 J/kg·K

Q = mcΔT = 2 × 4186 × (75 - 25) = 418600 J

Example 2

A 500 g metal requires 2000 J to raise its temperature by 10°C. Find its specific heat.

c = Q / (mΔT) = 2000 / (0.5 × 10) = 400 J/kg·K

Experimental Determination (Calorimetry Method)

Principle of Calorimetry:

Heat lost = Heat gained

Procedure:

Use a calorimeter, heat a substance, place it in the calorimeter, measure equilibrium temperature, and use the equation to solve.

Conclusion:

Specific Heat Capacity is a crucial thermodynamic concept that helps us understand the thermal behavior of different materials. It forms the foundation for real-world applications such as climate science, engineering, and even daily cooking.