Thermal Physics B Common Exam Traps

Scope

Gas-law conditions, the collision derivation, the exact mean molecular kinetic-energy relation, internal energy and the first law are core. Detailed p–V paths/cycles, named thermodynamic processes and rms-speed extensions are enrichment/supporting material.

Core derivation traps

In $pV=\frac{1}{3}Nm⟨c^2⟩$, the factor $1/3$ comes from isotropy: $⟨c_x^2⟩=⟨c^2⟩/3$. Do not confuse mean square speed $⟨c^2⟩$ with $⟨c{⟩}^2$, and do not confuse particle number $N$ with amount $n$ in moles.

Support note: This page supports Thermal Physics B by collecting common mistakes and exam traps.

Overview

This page highlights common mistakes made in Thermal Physics B questions. Most lost marks come from:

• wrong sign conventions
• misuse of Kelvin
• confusing state properties with transfer quantities
• incorrect p–V graph interpretation
• wrong ideal-gas assumptions

Use this page as a final revision checklist.

Related hub:

Thermal Physics B

Definition

An exam trap is a predictable error caused by mixing up thermal definitions, using the wrong sign convention, or treating path-dependent quantities like state properties.

Why It Matters

Thermal Physics B is heavy on interpretation. Many answers fail not because the equations are difficult, but because the student identifies the wrong process or attaches the wrong physical meaning to $Q$, $W$, $\Delta U$, or p–V graph area.

Key Representations

Core Ideas

• Thermal Physics B errors usually come from mixing state properties with transfer quantities.
• Kelvin is required in gas-law and kinetic-theory equations.
• The sign of work depends on whether work is defined as done on or by the gas.
• p-V area represents work, not internal energy.
• Process labels such as isothermal and adiabatic impose different energy constraints.

Exam Relevance

Use this support note as a final checklist before exam practice on kinetic theory, ideal gases, first-law questions, thermodynamic processes, and p-V diagrams.

1. Internal Energy vs Heat

Trap

Thinking heat is the same as internal energy.

Correction

• Internal energy = energy stored microscopically in system
• Heat = energy transferred because of temperature difference

Heat is a transfer process, not stored energy.

2. Celsius Instead of Kelvin

Trap

Using ${}^{\circ }\text{C}$ directly in gas laws or kinetic theory.

Wrong

$$\frac{P_1}{30}=\frac{P_2}{60}$$

Correct

Convert first:

$$30^{\circ }\mathrm{C}=303\mathrm{K},60^{\circ }\mathrm{C}=333\mathrm{K}$$

Use Kelvin in:

• gas laws
• ideal gas equation
• rms speed
• average kinetic energy relations

3. Wrong First-Law Sign Convention

Trap

Using work done by gas as positive when the syllabus equation uses work done on gas.

Required Convention

$$\Delta U=Q+W$$

Where:

• $Q>0$: heat supplied to gas
• $W>0$: work done on gas

Therefore

Expansion:

$$W<0$$

Compression:

$$W>0$$

4. Enrichment: area under a p–V graph gives internal energy

Trap

Thinking graph area gives internal energy change.

Correction

Area under a p–V graph gives pressure-volume work, not internal energy. In general use $p_{\mathrm{ext}}$ for boundary work; for a quasistatic path, $p_{\mathrm{gas}}=p_{\mathrm{ext}}$ and the plotted gas pressure may be used. The sign depends on direction and on whether work is defined as done by or on the gas.

$$W_{\mathrm{on}}=-\int p_{\mathrm{ext}}dV$$

Internal energy must be found using:

$$\Delta U=Q+W$$

or temperature change.

5. Enrichment: same endpoints mean same work

Trap

Assuming two different paths between same states give same work.

Correction

Work depends on path.

Different curves between same endpoints usually have different enclosed areas beneath them.

But

Temperature and internal energy are state quantities: their changes depend on the endpoints. Heat and work are transfer quantities and depend on the path.

6. Isothermal Means No Heat Transfer

Trap

If temperature is constant, assuming $Q=0$.

Correction

For an ideal gas of fixed amount and composition:

$$\Delta U=0$$

So:

$$Q=-W$$

Heat transfer may occur even when temperature is constant.

7. Adiabatic Means Constant Temperature

Trap

Confusing adiabatic with isothermal.

Correction

Adiabatic means:

$$Q=0$$

Temperature often changes.

• adiabatic expansion → cools
• adiabatic compression → heats

8. Constant Pressure Means No Work

Trap

If pressure is constant, assuming work is zero.

Correction

If volume changes:

$$W=-P\Delta V$$

Only constant volume guarantees zero work.

9. Vertical Line Means Pressure Constant

Trap

Misreading p–V graphs.

Correction

On p–V graph:

• vertical line → constant volume
• horizontal line → constant pressure

Remember axis labels.

10. RMS Speed = Mean Speed

Trap

Assuming:

$$v_{\text{rms}}=\bar{v}$$

Correction

RMS speed is based on squared speeds:

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

Usually:

$$v_{\text{rms}}>\bar{v}$$

11. Heavier Molecules Move Faster at Same Temperature

Trap

Thinking larger mass means larger speed.

Correction

At same temperature:

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

So:

• larger molar mass $M$ → lower speed
• lighter molecules move faster

12. Internal Energy of Ideal Gas Depends on Pressure Alone

Trap

Saying increasing pressure always increases internal energy.

Correction

For a monatomic ideal gas:

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

Internal energy depends on temperature only for a fixed amount in this monatomic model.

Pressure may increase because:

• temperature increased
• or volume decreased

These are different situations.

13. Evaporation Only Happens at Boiling Point

Trap

Thinking liquid evaporates only when boiling.

Correction

Evaporation occurs at any temperature from the surface.

Boiling occurs:

• throughout liquid
• at boiling point (for given pressure)

14. Latent Heat Raises Temperature

Trap

Thinking energy supplied during melting or boiling increases temperature.

Correction

During a phase change of a pure substance at fixed pressure while both phases coexist:

• temperature is constant
• energy increases intermolecular potential energy

15. Closed Cycle Means Zero Work

Trap

Since gas returns to original state, assuming no work is done.

Correction

For a cycle:

$$\Delta U=0$$

But net work may be non-zero.

Its magnitude equals the enclosed area of the loop.

For the usual p-V graph convention, a clockwise loop gives positive net work done by the gas. With this wiki’s first-law convention, work done on the gas has the opposite sign.

16. Forgetting Units

Trap

Using inconsistent SI units.

Convert to:

• $P$: Pa
• $V$: m${}^3$
• $T$: K
• energy: J
• molar mass: kg mol${}^{-1}$

17. Quick Checklist Before Submitting

Gas Law Questions

• converted to Kelvin?
• SI units used?
• constant quantity identified?

First Law Questions

• correct sign of $Q$?
• correct sign of $W$?
• used:

$$\Delta U=Q+W$$

p–V Graph Questions

• read axes correctly?
• expansion or compression?
• area = work, not internal energy?

Kinetic Theory Questions

• particle explanation included?
• mention collisions, kinetic energy, and intermolecular forces?

Links

• Thermal Physics B
• Kinetic Theory and Ideal Gases
• First Law and Thermodynamic Processes
• p-V Diagrams and Cycles

Summary

Most Thermal Physics B mistakes come from process misidentification and sign confusion. If you keep state properties, transfer quantities, and p–V graph meanings separate, the chapter becomes much more manageable.