Chapter 4: Heat

Overview

This chapter explores the fundamental concepts of heat and thermal physics, which are essential for understanding energy transfer, temperature changes, and the behavior of gases. Heat is a form of energy that flows from objects at higher temperatures to objects at lower temperatures, and this chapter covers the principles that govern this energy transfer, including thermal equilibrium, specific heat capacity, latent heat, and gas laws.

Learning Objectives

After completing this chapter, you will be able to:

• Understand the concept of thermal equilibrium and its applications
• Calculate heat transfer using specific heat capacity formulas
• Differentiate between specific heat capacity and heat capacity
• Apply the concept of latent heat to phase changes
• Solve problems involving gas laws (Boyle's, Charles', and Pressure laws)
• Convert between Celsius and Kelvin temperature scales
• Analyze real-world applications of heat and thermal physics

Thermal Equilibrium

Main Concept

Thermal equilibrium is achieved when two objects in thermal contact have no net heat flow between them. At this point, both objects have the same temperature. Heat flows from regions of higher temperature to regions of lower temperature.

Key Principles

• Heat flows from hot objects to cold objects
• When thermal equilibrium is reached, net heat flow is zero
• Temperature is the measure of the average kinetic energy of particles in a substance

Important Terms

• Temperature: Measure of the degree of hotness of an object
• Heat: Energy transferred from a hot object to a cold object
• Thermal Contact: Condition where heat energy can transfer between two objects

Did You Know?

The principle of thermal equilibrium is used in thermometers to measure temperature. When a thermometer reaches thermal equilibrium with the object being measured, it shows the correct temperature.

Specific Heat Capacity

Main Concept

Specific heat capacity (c) of a substance is the amount of heat required to raise the temperature of 1 kg of the substance by 1°C or 1 K.

Key Principles

• Materials with high specific heat capacity require more heat to increase their temperature (heat up slowly) and release more heat when cooling (cool down slowly)
• Water has a very high specific heat capacity (4200 J kg⁻¹ K⁻¹), which is why it's used as a coolant

Key Formulas

$$Q = mcΔθ$$

Where:

• Q = Quantity of heat (Joules, J)
• m = Mass (kilograms, kg)
• c = Specific heat capacity (J kg⁻¹ K⁻¹)
• Δθ = Change in temperature (Kelvin, K)

For electrical heating:

$$P = V \times I$$ $$Pt = mcΔθ \text{ (assuming no heat loss to surroundings)}$$

Where:

• P = Power (Watts, W)
• t = Time (seconds, s)

Important Terms

• Heat Capacity: Amount of heat required to raise the temperature of an object by 1°C. C = Q/Δθ

Worked Example

Problem: A 2 kg block of iron requires 18,400 J of heat to raise its temperature from 20°C to 80°C. Calculate the specific heat capacity of iron.

Solution:

• Mass, m = 2 kg
• Heat, Q = 18,400 J
• Temperature change, Δθ = 80°C - 20°C = 60 K

Using Q = mcΔθ:

$$c = \frac{Q}{mΔθ} = \frac{18,400}{2 \times 60} = 153.33 \text{ J kg}^{-1} \text{K}^{-1}$$

Answer: The specific heat capacity of iron is 153.33 J kg⁻¹ K⁻¹.

Specific Latent Heat

Main Concept

Latent heat is the heat absorbed or released during a phase change (e.g., solid to liquid, liquid to gas) at constant temperature.

Key Principles

• Specific Latent Heat of Fusion (L_f): Heat required to change 1 kg of substance from solid to liquid without temperature change
• Specific Latent Heat of Vaporization (L_v): Heat required to change 1 kg of substance from liquid to gas without temperature change

Key Formulas

$$Q = mL$$ $$Pt = mL \text{ (during phase change)}$$

Where:

• Q = Quantity of heat (Joules, J)
• m = Mass (kilograms, kg)
• L = Specific latent heat (J kg⁻¹)

Important Terms

• Melting: Solid to liquid
• Boiling: Liquid to gas
• Condensation: Gas to liquid
• Freezing: Liquid to solid

Latent Heat Values

Gas Laws

Main Concept

Gas laws describe the relationships between pressure (P), volume (V), and temperature (T) for a fixed mass of gas.

Boyle's Law

Principle: For a fixed mass of gas at constant temperature, pressure is inversely proportional to volume.

Formula:

$$P_1V_1 = P_2V_2$$

Graph: P vs 1/V is a straight line passing through origin.

Charles's Law

Principle: For a fixed mass of gas at constant pressure, volume is directly proportional to absolute temperature.

Formula:

$$\frac{V_1}{T_1} = \frac{V_2}{T_2}$$

Graph: V vs T is a straight line with positive slope.

Pressure Law

Principle: For a fixed mass of gas at constant volume, pressure is directly proportional to absolute temperature.

Formula:

$$\frac{P_1}{T_1} = \frac{P_2}{T_2}$$

Combined Gas Law:

$$\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$$

Important Terms

• Absolute Temperature: Temperature scale where absolute zero (0 K) is the lowest possible temperature
• Absolute Zero: Temperature at which particles have minimum kinetic energy
• Kelvin Scale: T(K) = θ(°C) + 273.15

Temperature Conversion

Kelvin-Celsius Conversion

$$T(K) = θ(°C) + 273.15$$ $$θ(°C) = T(K) - 273.15$$

SPM Exam Tips

Common Mistakes to Avoid

1. Forcing Suffixes: Always include units in your calculations
2. Temperature Scales: Remember to use Kelvin for gas laws
3. Phase Changes: Remember that temperature remains constant during phase changes
4. Heat vs Temperature: Heat is energy transfer, temperature is measure of hotness

Problem-Solving Strategies

1. Identify the Process: Determine if heat transfer, phase change, or gas law problem
2. List Given Data: Write down all known quantities with units
3. Choose Appropriate Formula: Select the right equation for the situation
4. Check Units: Ensure all units are consistent (use Kelvin for gas laws)
5. Verify Results: Check if answer makes physical sense

Important Formulas Summary

Practical Applications

Real-World Examples

1. Cooling Systems: Water's high specific heat capacity makes it effective for cooling engines
2. Cooking: Understanding heat capacity helps in choosing appropriate cooking methods
3. Weather: Sea breezes result from different heat capacities of land and water
4. Refrigeration: Uses latent heat to remove heat from food
5. Weather Balloons: Expand as they rise due to decreasing atmospheric pressure (Charles's Law)

Safety Considerations

• Thermal Burns: Understanding heat transfer helps prevent burns
• Pressure Vessels: Gas laws are crucial for designing safe containers
• Fire Safety: Knowledge of heat transfer principles aids in fire prevention

Summary

This chapter covered essential concepts in thermal physics:

• Thermal Equilibrium: Heat flows until temperatures equalize
• Specific Heat Capacity: Heat required per kg per degree temperature change
• Latent Heat: Heat absorbed/released during phase changes
• Gas Laws: Relationships between pressure, volume, and temperature

Master these concepts to understand energy transfer, phase changes, and gas behavior - fundamental to many physics applications and engineering systems.

Practice Questions

1. A 500 g copper block is heated from 20°C to 100°C. Calculate the heat required. (c_copper = 400 J kg⁻¹ K⁻¹)

2. How much heat is needed to convert 2 kg of ice at 0°C to water at 0°C? (L_f = 3.34 × 10⁵ J kg⁻¹)

3. A gas occupies 3 $m^3$ at 300 K and 1 atm pressure. What volume will it occupy at 400 K and 2 atm pressure?

4. Explain why coastal areas have more moderate temperatures than inland areas.

---

• Chapter 3: Forces and Pressure
• Chapter 5: Waves