First Law of Thermodynamics

CIE A-Level Physics· Topic 20: Thermodynamics· 20 min read

1. Core Definition and CIE Sign Convention★★☆☆☆⏱ 5 min

🚫 No Calculator

📘 Definition

First Law of Thermodynamics

\Delta U = Q - W

A restatement of the principle of conservation of energy for thermal processes, relating the change in a system's internal energy to heat added to the system and work done by the system.

Example:

Positive values indicate energy added to the system (Q) or work done by the system (W) per CIE 9702 convention.

📐 Worked Example

A gas absorbs 250 J of heat from its surroundings and does 130 J of work on the surroundings. Calculate the change in internal energy of the gas.

1
Identify values with CIE convention:
2
Heat enters the system, so $Q = + 250$ J. Work is done by the system, so $W = + 130$ J.
3
Substitute into the first law equation:
4
$\Delta U = Q - W = 250 - 130$
5
Calculate the result: $Δ U = + 120$ J

2. Application to Common Thermal Processes★★★☆☆⏱ 8 min

🚫 No Calculator

The first law simplifies for different standard processes that are commonly tested in CIE exams. We can fix one variable to get a simpler relationship between the remaining terms.

📘 Definition

Adiabatic Process

A thermal process where no heat is exchanged between the system and surroundings. This occurs for rapid expansions/compressions where there is no time for heat transfer.

Example:

Adiabatic processes always have $Q = 0$ by definition.

Process Name	Key Condition	Simplified First Law
Constant Volume (Isochoric)	$W = 0$ (no work done)	$Δ U = Q$
Adiabatic	$Q = 0$ (no heat transfer)	$Δ U = - W$
Isothermal (ideal gas)	$Δ U = 0$ (constant temperature)	$Q = W$
Free Expansion	$Q = 0, W = 0$	$Δ U = 0$

📐 Worked Example

An ideal gas undergoes adiabatic compression. 400 J of work is done on the gas by the surroundings. Calculate the change in internal energy.

1
Adiabatic process means no heat transfer: $Q = 0$
2
Work is done on the gas, so work done by the gas is negative: $W = - 400$ J
3
Substitute into first law:
4
$\Delta U = Q - W = 0 - (-400) = +400$
5
Conclusion: Internal energy of the gas increases by 400 J, so its temperature rises.

Exam tip:

Always check if the question tells you work is done on or by the gas, and adjust the sign of W accordingly.

3. First Law on p-V Diagrams★★★☆☆⏱ 7 min

✓ Calculator OK

CIE frequently asks questions about processes plotted on pressure-volume (p-V) diagrams. The magnitude of work done by the gas equals the area under the process curve on a p-V diagram.

If the process moves from left to right (volume increases), the gas expands, so W is positive. If it moves right to left (volume decreases), the gas is compressed, so W is negative.

📐 Worked Example

A gas expands at constant pressure of 2 Pa from $V = 1 m^{3}$ to $V = 4 m^{3}$ . 10 J of heat is added to the gas during the expansion. Calculate the change in internal energy.

1
Calculate work done by the gas for constant pressure: $W = p Δ V$
2
$W = 2 \times (4 - 1) = 6 \text{ J}$
3
We know $Q = + 10$ J (heat added)
4
Apply first law:
5
$\Delta U = Q - W = 10 - 6 = +4 \text{ J}$
6
Final answer: internal energy increases by 4 J

4. Common Pitfalls

Wrong move:

Using the 'work done on the system' convention instead of CIE's convention.

Why:

Different sources use different conventions, but CIE 9700 strictly uses work done by the system.

Correct move:

Always use $Δ U = Q - W$ where W is positive when work is done by the system.

Wrong move:

Assuming $Δ U = 0$ for any expansion process.

Why:

Internal energy only stays constant for isothermal expansion of an ideal gas, not adiabatic expansion.

Correct move:

Only set $Δ U = 0$ if the process is explicitly stated to be isothermal.

Wrong move:

Using $W = p Δ V$ for non-constant pressure processes.

Why:

This formula only holds when pressure is constant. For changing pressure, work equals area under the p-V curve.

Correct move:

Calculate the area under the process curve to find W before applying the first law.

Wrong move:

Taking Q as positive when heat leaves the system.

Why:

Sign conventions for Q are often mixed up with W.

Correct move:

Q is positive when heat enters the system, negative when heat leaves the system.

5. Quick Reference Cheatsheet

Concept	CIE Convention	Equation
First Law	ΔU = change in internal energy, Q = heat added, W = work done BY system	$Δ U = Q - W$
Constant Volume	No work done	$Δ U = Q$
Adiabatic	No heat exchange	$Q = 0 \to Δ U = - W$
Isothermal (ideal gas)	Constant internal energy	$Δ U = 0 \to Q = W$
p-V Work	Expansion (left→right) = W positive	Area under curve = \|W\|
Full Cycle	Returns to start state	$Δ U = 0 \to Q = W$

When this came up on past exams

AI-estimated based on syllabus patterns — cross-check with official past papers for accuracy. Use only as revision-focus signals.

2022 · 12
First law sign convention MCQ
2023 · 22
Adiabatic process calculation
2024 · 11
p-V cycle energy change

Going deeper

syllabusCIE 9702 Official SyllabusTopic 20 reference

What's Next

Mastering the first law of thermodynamics and its sign convention is critical for all higher thermal physics topics in CIE A-Level Physics. The principles you have learned here are applied to analyze engine efficiency, adiabatic and isothermal processes, and entropy changes. Consistent practice with sign conventions will help you avoid losing easy marks in both multiple choice and structured questions. Next, you will explore specific types of thermal processes in more detail before moving on to the second law of thermodynamics.