Thermal Physics B

Overview

Thermal Physics B studies the microscopic explanation of thermal behaviour and introduces thermodynamics. It explains how particle motion gives rise to pressure, temperature and internal energy, and how gases exchange energy through heating and work.

This topic builds directly on Thermal Physics A.

It is the continuation of the thermal syllabus into kinetic theory and thermodynamics.

You should be able to:

• explain internal energy using particle ideas
• apply gas laws and the ideal gas equation
• relate temperature to molecular kinetic energy
• analyse thermodynamic processes
• interpret p–V diagrams
• solve first-law energy problems

Boundary reminder:

• this page focuses on particle models, gas behaviour, and thermodynamic processes
• thermometer calibration, calorimetry, latent heat, heating curves, and electrical thermal methods belong mainly to Thermal Physics A

Core Ideas

Thermal Physics B is built around four ideas:

1. Particle motion explains temperature, pressure, phase behaviour, and internal energy.
2. The ideal-gas model gives simple laws linking pressure, volume, and temperature.
3. Internal energy is a state property, while heat and work are energy-transfer processes.
4. Thermodynamic processes and p-V diagrams organise how gases change from one state to another.

Exam Relevance

This chapter is conceptually dense and calculation-heavy. Many exam errors come from mixing up heat with internal energy, using Celsius instead of kelvin, or applying the wrong sign convention for work. Clear process identification is often the difference between a correct and incorrect answer.

1. Kinetic Theory Overview

Core Model

Matter is made of atoms or molecules in constant random motion.

Macroscopic properties arise from microscopic behaviour:

• temperature ↔ average random kinetic energy
• pressure ↔ collisions with container walls
• phase ↔ intermolecular spacing and bonding
• internal energy ↔ total microscopic energy stored

For a fuller treatment of particle models, gas laws, ideal-gas assumptions, and rms speed, see Kinetic Theory and Ideal Gases.

Figure 1. The particle model is the starting point because it explains why internal energy can change without a temperature rise.

2. Internal Energy

Here internal energy is treated at the microscopic and thermodynamic level. For the macroscopic language of heat transfer and calorimetry, refer back to Thermal Physics A.

Definition

Internal energy $U$ is the sum of:

• total random kinetic energy of particles
• total intermolecular potential energy

$$U=K{E}_{\text{random,total}}+P{E}_{\text{intermolecular,total}}$$

State Property

Internal energy depends only on the state of the system:

• pressure $P$
• volume $V$
• temperature $T$
• amount of particles $n$

It does not depend on the path taken to reach that state.

3. Changes of State and Evaporation

Melting / Boiling at Constant Temperature

During melting or boiling:

• energy supplied weakens intermolecular attractions
• potential energy increases
• average kinetic energy unchanged

Therefore temperature stays constant.

Why Specific Latent Heat of Vaporisation is Larger

For the same substance:

$$l_v>l_f$$

where:

• $l_v$ = specific latent heat of vaporisation
• $l_f$ = specific latent heat of fusion

This is because vaporisation requires:

• almost complete separation of molecules
• a much larger increase in intermolecular potential energy
• expansion work against the surroundings

Cooling by Evaporation

Fastest molecules escape first.

Remaining liquid has lower average kinetic energy.

Hence:

• temperature falls
• evaporation causes cooling

Examples:

• sweating
• perfume evaporating
• alcohol wipes cooling skin

4. Ideal Gases

Ideal Gas Assumptions

An ideal gas is a model where:

1. molecules occupy negligible volume
2. intermolecular forces are negligible
3. collisions are perfectly elastic
4. molecules move randomly
5. molecules obey Newtonian mechanics

Real gases behave more ideally at:

• high temperature
• low pressure

Gas Pressure from Collisions

Pressure is caused by molecules repeatedly colliding with container walls and changing momentum.

More frequent or harder collisions produce higher pressure.

5. Gas Laws

Boyle’s Law (constant temperature)

$$P\propto \frac{1}{V}$$ $$P_1{V}_1=P_2{V}_2$$

Charles’ Law (constant pressure)

$$V\propto T$$ $$\frac{V_1}{T_1}=\frac{V_2}{T_2}$$

Pressure Law (constant volume)

$$P\propto T$$ $$\frac{P_1}{T_1}=\frac{P_2}{T_2}$$

Important Note

Use Kelvin in all gas-law calculations.

Figure 2. The ideal gas laws are not separate facts; they are the same ideal-gas relation seen from different fixed variables.

In ideal gas law, the temperature must be expressed in Kelvin unit. The Kelvin reading is obtained by adding 273.15 to the Celsius reading.

If a temperature has Celsius value $T_{{}^{\circ }\mathrm{C}}$, then its Kelvin value is:

$$T_{\mathrm{K}}=T_{{}^{\circ }\mathrm{C}}+273.15$$

Examples:

• $0^{\circ }\mathrm{C}\to 273.15\mathrm{K}$
• $25^{\circ }\mathrm{C}\to 298.15\mathrm{K}$
• $100^{\circ }\mathrm{C}\to 373.15\mathrm{K}$

A temperature interval has the same numerical value on both scales:

$$\Delta T=100^{\circ }\mathrm{C}=100\mathrm{K}$$

The full ideal-gas development, including mole relations and internal energy of an ideal gas, is expanded in Kinetic Theory and Ideal Gases.

6. Ideal Gas Equation

Combining gas laws:

$$PV=nRT$$

Where:

• $P$: pressure
• $V$: volume
• $n$: moles
• $R$: molar gas constant
• $T$: Kelvin temperature

Alternative form:

$$PV=NkT$$

Where:

• $N$: number of molecules
• $k$: Boltzmann constant

7. Mole Concept

Avogadro Constant

$$N_A=6.02\times 10^{23}{\text{mol}}^{-1}$$

One mole contains $N_A$ particles.

$$N=n{N}_A$$

Relationship:

$$R=N_{A}k$$

8. Internal Energy of an Ideal Gas

For an ideal gas:

• intermolecular forces negligible
• potential energy ≈ 0

So internal energy is purely kinetic.

For monatomic ideal gas:

$$U=\frac{3}{2}NkT=\frac{3}{2}nRT=\frac{3}{2}PV$$

Key Result

Internal energy is the total microscopic kinetic and potential energy of the particles in a system. For an ideal gas, intermolecular forces are neglected, so the internal energy is the sum of the kinetic energies of all particles, which depends only on temperature.

At constant temperature:

$$\Delta U=0$$

9. RMS Speed

Definition

Root mean square speed:

$$v_{\text{rms}}=\sqrt{\frac{v_1^2+v_2^2+\cdots +v_N^2}{N}}$$

Formula

$$\frac{1}{2}m{v}_{\text{rms}}^2=\frac{3}{2}kT$$

Hence:

$$v_{\text{rms}}=\sqrt{\frac{3kT}{m}}$$

or

$$v_{\text{rms}}=\sqrt{\frac{3RT}{M}}$$

Where $M$ is molar mass.

Trends

• higher $T$ → higher $v_{\text{rms}}$
• lower mass → higher $v_{\text{rms}}$

10. Work Done by Gas

Formula

Work done on gas:

$$W_{\text{on gas}}=-\int PdV$$

Interpretation

Compression

• volume decreases
• surroundings do work on gas

$$W>0$$

Expansion

• gas does work on surroundings

$$W<0$$

p–V Graph Meaning

Magnitude of work done = area under graph.

Figure 3. On a p–V diagram, the magnitude of the work equals the area under the path, while the sign depends on the direction of the process.

11. First Law of Thermodynamics

$$\Delta U=Q+W$$

Where:

• $\Delta U$: change in internal energy
• $Q$: heat supplied to system
• $W$: work done on system

Sign Convention

Heat

• into system: $Q>0$
• out of system: $Q<0$

Work

• on gas: $W>0$
• by gas: $W<0$

For a deeper treatment of sign convention, worked first-law problems, and standard process reasoning, see First Law and Thermodynamic Processes.

Figure 4. The first law tracks energy into the system as heat or work and converts it into a change in internal energy.

12. Thermodynamic Processes

Isochoric (constant volume)

$$W=0,\Delta U=Q$$

Pressure and temperature may change.

Isobaric (constant pressure)

$$W=-P\Delta V$$

Isothermal (constant temperature, ideal gas)

$$\Delta U=0,Q=-W$$

Adiabatic

No heat transfer.

$$Q=0,\Delta U=W$$

Usually caused by rapid change or insulation.

Figure 5. For the same initial state, an adiabatic p–V curve is steeper than an isothermal curve.

These process types are developed in more detail, with process-by-process energy interpretation, in First Law and Thermodynamic Processes.

13. Cyclic Processes

Gas returns to original state.

Therefore:

$$\Delta U=0$$

So:

$$Q_{\text{net}}=-W_{\text{net}}$$

The magnitude of the net work equals the enclosed area on the p–V graph.

Used in heat engines and refrigerators.

Figure 6. A closed cycle returns to the starting state, so only the enclosed area survives as net work.

14. p–V Diagram Interpretation

Common Shapes

• horizontal line → constant pressure
• vertical line → constant volume
• rectangular hyperbola → isothermal
• steeper curve → adiabatic

Area Rules

• area under path = magnitude of the work along that path
• enclosed loop = magnitude of the net work over the cycle

With the sign convention used here, a clockwise loop means the gas does net work on the surroundings, so $W_{\text{net}}<0$.

For detailed p-V graph reading, work-from-area arguments, and cycle interpretation, see p-V Diagrams and Cycles.

15. Worked Examples

Example 1: Ideal Gas Equation

A gas has:

• $P=2.0\times 10^5\mathrm{Pa}$
• $V=3.0\times 10^{-3}{\mathrm{m}}^3$
• $T=300\mathrm{K}$

Find $n$.

$$PV=nRT$$ $$n=\frac{PV}{RT}=\frac{(2.0\times 10^5)(3.0\times 10^{-3})}{8.31(300)}=0.24\mathrm{mol}$$

Example 2: First Law of Thermodynamics

A gas absorbs $150\mathrm{J}$ of heat and expands, doing $60\mathrm{J}$ of work on the surroundings.

Using the sign convention:

$$\Delta U=Q+W$$

where $W$ is the work done on the gas.

Since the gas does work on the surroundings, the work done on the gas is:

$$W=-60\mathrm{J}$$

Hence:

$$\Delta U=150-60=90\mathrm{J}$$

Example 3: Constant-Volume Heating

At constant volume, there is no volume change, so no pressure-volume work is done:

$$W=0$$

If $80\mathrm{J}$ of heat is supplied:

$$\Delta U=Q+W=80+0=80\mathrm{J}$$

16. Formula Summary

Boyle’s Law (constant temperature)

$$P_1{V}_1=P_2{V}_2$$

Charles’s Law (constant pressure)

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

Pressure Law (constant volume)

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

Ideal Gas Equations

$$PV=nRT$$ $$PV=NkT$$

Mole Relations

$$N=n{N}_A$$ $$R=N_{A}k$$

Internal Energy of a Monatomic Ideal Gas

$$U=\frac{3}{2}nRT$$

RMS Speed

$$v_{\text{rms}}=\sqrt{\frac{3RT}{M}}$$

First Law of Thermodynamics

Using the convention that $W$ is the work done on the gas:

$$\Delta U=Q+W$$

For pressure-volume work:

$$W=-\int PdV$$

17. Common Exam Pitfalls

• using Celsius instead of Kelvin
• wrong sign for work done by gas
• thinking heat is internal energy
• assuming all gases are ideal always
• thinking p–V area gives internal energy
• forgetting $\Delta U=0$ in a cycle
• forgetting $\Delta U=0$ in isothermal ideal gas process
• confusing rms speed with mean speed

For a focused revision checklist of these errors, see Thermal Physics B Common Exam Traps.

Links

• Kinetic Theory and Ideal Gases
• First Law and Thermodynamic Processes
• p-V Diagrams and Cycles
• Thermal Physics B Common Exam Traps
• Thermal Physics A
• Work, Energy and Power

Summary

Thermal Physics B explains how microscopic particle behaviour connects to macroscopic gas laws and thermodynamic energy changes. Strong performance comes from keeping state properties, transfer quantities, and process conditions clearly separated.