What is the first law of thermodynamics in Physics?

The first law of thermodynamics, often referred to as the law of energy conservation, states that energy cannot be created or destroyed in an isolated system. It can only be transformed from one form to another. In the context of thermodynamics, this means the total energy of a system and its surroundings remains constant. This principle is fundamental in Physics and is particularly emphasized in the Cambridge International A Levels curriculum.

How is the first law of thermodynamics mathematically expressed?

The first law of thermodynamics is mathematically expressed as ΔU = Q - W, where ΔU represents the change in internal energy of a system, Q is the heat added to the system, and W is the work done by the system. This equation highlights the relationship between heat transfer, work, and internal energy changes, which is a key concept in Physics and thermodynamics studies at the Cambridge International A Levels.

What are some practical examples of the first law of thermodynamics?

Practical examples of the first law of thermodynamics include the operation of heat engines, refrigerators, and air conditioners. In a heat engine, for instance, chemical energy from fuel is converted into thermal energy and then into mechanical work. Similarly, refrigerators use work to transfer heat from a cooler to a warmer place, demonstrating energy conservation. These examples are crucial for understanding thermodynamics in the Cambridge International A Levels Physics curriculum.

How does the first law of thermodynamics apply to closed systems?

In a closed system, the first law of thermodynamics implies that any change in the system's internal energy is due to heat exchange and work done. Since no mass enters or leaves a closed system, the energy changes are solely due to these two factors. This concept is vital for solving problems related to energy conservation in closed systems, a common topic in Cambridge International A Levels Physics.

What is the significance of the first law of thermodynamics in scientific studies?

The first law of thermodynamics is significant because it establishes the principle of energy conservation, which is a cornerstone of all scientific studies involving energy transformations. It provides a framework for analyzing energy exchanges in physical and chemical processes, making it essential for students studying Physics, particularly those preparing for the Cambridge International A Levels. Understanding this law helps in comprehending more complex thermodynamic processes and systems.

Why is "Sign confusion for work" a common mistake in The first law of thermodynamics?

Why it happens: Different sign conventions in textbooks. How to avoid it: Cambridge convention: W is work done ON gas. Work done BY gas is -W. State convention clearly. Source: 9702 Examiner Reports 2022-2024

ThermodynamicsCambridge International A Level Physics 9702

The first law of thermodynamics

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Short Study Notes — The first law of thermodynamics

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First Law Study Notes — Cambridge International A Level Physics 9702 (2025-2027 syllabus)

$\Delta U = q + W$ . Energy conservation for thermodynamic systems.

What you’ll learn

Mapped to the Cambridge International A Level 9702 syllabus (2025-2027).

16.2.1 — State and apply 1st law.
16.2.2 — Identify processes (isothermal, adiabatic).

First law

$\Delta U = q + W$ .

Statement. Change in internal energy = heat added + work done ON system. $\Delta U = q + W$

Cambridge sign convention.

$q > 0$ : heat added TO system.
$W > 0$ : work done ON system.

Energy conservation. Any change in $U$ must come from heat or work.

Common processes.

Isothermal: $T$ constant → $\Delta U = 0$ (ideal gas) → $q = -W$ .
Adiabatic: $q = 0$ → $\Delta U = W$ .
Constant volume: $W = 0$ → $\Delta U = q$ .
Constant pressure: $W = -p\Delta V$ .

Example. Gas absorbs 200 J heat, work 80 J done on it: $\Delta U = 200 + 80 = 280$ J.

Cambridge tip. State sign convention explicitly.

The first law states that the change in internal energy equals the heat added to the system plus the work done on it.

$\Delta U = q + W$ .
Sign convention clear.
Process types.

See the full worked example for the first law of thermodynamics →

How it’s examined

First law central to A2. Most-tested: first-law calculation (6 marks), isothermal/adiabatic (6 marks).

Sources: Cambridge International A Level Physics 9702 syllabus (2025-2027); 9702 Examiner Reports 2022-2024; 9702/42 May/Jun 2024 question paper and mark scheme. Last reviewed 2026-05-11.

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Step-by-step worked examples — The first law of thermodynamics

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1First law (6 marks)
Extended• Adapted from 9702/42 May/Jun 2024• first law
Question
A gas absorbs 200 J heat and 80 J work is done ON it. Find change in internal energy. (6 marks)
Step-by-step solution
1. Step 1
  $\Delta U = q + W$ . $q$ = heat absorbed (positive). $W$ = work done ON gas (positive).
2. Step 2
  Substitute.
  $\Delta U = 200 + 80 = 280 \text{ J}$
Answer
$\Delta U = 280$ J.
2Isothermal process (6 marks)
Extended• isothermal
Question
An ideal gas expands isothermally absorbing 500 J of heat. Find $\Delta U$ and work done ON gas. (6 marks)
Step-by-step solution
1. Step 1
  Isothermal: $T$ constant → $\Delta U = 0$ for ideal gas.
2. Step 2
  $\Delta U = q + W \Rightarrow W = -q$ .
  $W = -500 \text{ J}$
3. Step 3
  Interpretation. Work done ON gas is $-500$ J; gas does $+500$ J work on surroundings.
Answer
$\Delta U = 0$ . $W_{\text{on gas}} = -500$ J (gas does 500 J on surroundings).

Key Formulae — The first law of thermodynamics

The formulae you need to memorise for the first law of thermodynamics on the Cambridge International A Level 9702 paper, with every variable defined in plain English and a note on when to use it.

First law of thermodynamics
$\Delta U = q + W$
$q$
heat ADDED to system
$W$
work done ON system
When to use
Conservation of energy for thermodynamic system. Sign convention: $q > 0$ if heat added; $W > 0$ if work done ON gas.
Work in expansion
$W = -p\Delta V \quad (\text{work done ON gas at constant } p)$
When to use
Constant-pressure process. Gas expanding ( $\Delta V > 0$ ) means work done BY gas (negative $W$ on gas).

Key Definitions and Keywords — The first law of thermodynamics

Definitions to memorise and the exact keywords mark schemes credit for the first law of thermodynamics answers — sharpened from recent examiner reports for the 2026 Cambridge International A Level 9702 sitting.

First law of thermodynamics
Examiner keyword
Change in internal energy of a system equals heat added to system plus work done on system. $\Delta U = q + W$ .
Isothermal
Examiner keyword
Constant temperature. For ideal gas: $\Delta U = 0$ .
Adiabatic
Examiner keyword
No heat transfer ( $q = 0$ ). $\Delta U = W$ .

Common Mistakes and Misconceptions — The first law of thermodynamics

The traps other students keep falling into on the first law of thermodynamics questions — taken from recent Cambridge International A Level 9702 examiner reports and mark schemes — and how to avoid them.

✕Sign confusion for work
9702 Examiner Reports 2022-2024
Why it happens
Different sign conventions in textbooks.
How to avoid it
Cambridge convention: $W$ is work done ON gas. Work done BY gas is $-W$ . State convention clearly.

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