Why is internal energy called a state function?

Internal energy is a state function because its value depends only on the current thermodynamic state of the system (e.g., its temperature, pressure, and volume), not on the path taken to reach that state. This means if a system returns to its initial state, its internal energy returns to its initial value, regardless of the processes it underwent.

What is the difference between heat and internal energy?

Internal energy is the energy *stored within* a system due to the random motion and interaction of its particles. Heat (Q), on the other hand, is the *transfer of thermal energy* between systems or between a system and its surroundings due to a temperature difference. Heat is energy *in transit*, while internal energy is energy *contained*.

Does the First Law of Thermodynamics apply to all types of systems?

Yes, the First Law of Thermodynamics is a fundamental principle of energy conservation that applies to all thermodynamic systems, whether open, closed, or isolated, and to all types of processes, provided energy transfers are accounted for correctly as heat or work.

Can you summarize the First Law for different processes (isothermal, adiabatic, etc.)?

Certainly! For an **isovolumetric** process (constant volume), $W=0$ so $\Delta U = Q$. For an **isothermal** process (constant temperature), $\Delta U=0$ for an ideal gas, so $Q = -W$. For an **adiabatic** process (no heat transfer), $Q=0$ so $\Delta U = W$. For an **isobaric** process (constant pressure), all terms can be non-zero and $W = -p\Delta V$.

Where can I learn The first law of thermodynamics for Cambridge 9702?

This free lesson on MarkScheme covers syllabus point 16.2 (The first law of thermodynamics) for Cambridge A-Level Physics. It includes visual revision, key points, and links to real past-paper questions with mark-scheme marking at markscheme.app/courses/9702/16-2-the-first-law-of-thermodynamics.

Is The first law of thermodynamics (16.2) on 9702 free to study?

Yes. The Physics 9702 course on MarkScheme is 100% free — including premium visual lessons, exam tips, and past-paper marking. No paywall for The first law of thermodynamics.

The first law of thermodynamics 9702 — Free…

The first law of thermodynamics

Welcome to Thermodynamics, the fascinating study of heat and energy! Our first stop is understanding how a system's total energy content, called internal energy, can change. This is all captured by the foundational First Law of Thermodynamics, a universal principle of energy conservation. This pilot aligns with Senpai Corner A Level notes (2025–2027) for topic 16.2.

BY THE END, YOU CAN…

1Define internal energy and explain how it relates to temperature.
2State and apply the First Law of Thermodynamics (ΔU = Q + W).
3Interpret the signs of Q, W, and ΔU correctly in thermodynamic processes.
4Apply the First Law to isovolumetric, isothermal, and adiabatic processes.
5Calculate the work done by a gas during expansion at constant pressure (W = pΔV).

In simple terms

A friendly intro before the formal notes — no formulas yet.

The first law of thermodynamics

Cambridge 9702 Paper 4 — The first law of thermodynamics (16.2). Senpai Corner diagram-backed pilot with premium structure and live visuals.

1
$\Delta U$ (Change in Internal Energy):
2
+ $\Delta U$ : System's internal energy increases (e.g., temperature rises).
3
- $\Delta U$ : System's internal energy decreases (e.g., temperature falls).
4
$Q$ (Energy Transferred via Heating):

What this topic covers

The official Cambridge syllabus points this lesson works through.

16.2.1
Recall and use $W = pΔV$ for the work done when the volume of a gas changes at constant pressure and understand the difference between the work done by the gas and the work done on the gas
16.2.2
Recall and use the first law of thermodynamics $ΔU = q + W$ expressed in terms of the increase in internal energy, the heating of the system (energy transferred to the system by heating) and the work done on the system

Explore the concept

Use the live diagram and synced steps — play it or tap a step card to walk through.

Key formulas

Tap any symbol to reveal exactly what it means and its units.

$Work_{by} = p \Delta V$

Tap a symbol — great for exam definitions

$\Delta U = Q + W$

Tap a symbol — great for exam definitions

Full topic notes

Formal explanation with the rigour you need for the exam.

What is Internal Energy (U)?

Every substance is made up of countless particles (atoms or molecules) that are constantly moving and interacting. The internal energy (U) of a body is the total sum of all the random kinetic energies (due to particle motion) and potential energies (due to forces between particles) of these particles. It’s a 'state function', meaning its value depends only on the current condition of the system, not how it arrived at that state.

Temperature and Internal Energy

The absolute temperature of a system is a direct measure of the average kinetic energy of its constituent particles. If you increase a system's temperature, you increase the average kinetic energy of its particles, and consequently, its overall internal energy rises. For an ideal gas, the internal energy is directly proportional to its absolute temperature.

Work Done on or by a Gas (W)

Besides heating, the other way to change a system's internal energy is by doing work. For a gas in a cylinder with a movable piston, work is done when the volume of the gas changes. If the gas expands, it pushes the piston outwards, doing work on its surroundings. If the gas is compressed, the surroundings do work on the gas.

For a process occurring at a constant pressure $p$ , the work done by the gas as it expands by a volume $\Delta V$ is given by:

Work_{by} = p $\Delta V$

It's crucial to relate this to the term $W$ in the First Law equation, $\Delta U = Q + W$ . In the Cambridge A-Level Physics syllabus, $W$ represents the work done on the system. Therefore:

When a gas expands ( $\Delta V > 0$ ), it does positive work on the surroundings. The work done on the gas is negative: $W = -p \Delta V$ .
When a gas is compressed ( $\Delta V < 0$ ), the surroundings do positive work on the gas. The work done on the gas is positive: $W = -p \Delta V$ (since $\Delta V$ is negative, $W$ becomes positive).

Introducing the First Law of Thermodynamics

The First Law of Thermodynamics is a powerful restatement of the principle of conservation of energy. It tells us that energy cannot be created or destroyed, only transferred or transformed. For a thermodynamic system, energy can move in or out through two primary mechanisms: heating (Q) or work done (W). The law quantifies how these transfers affect the system's internal energy.

$\Delta U = Q + W$

This formula links the change in a system's internal energy ( $\Delta U$ ) to the heat energy transferred ( $Q$ ) and the work done ( $W$ ). Understanding the signs of each term is absolutely critical for solving problems correctly.

Deciphering the Signs: Q, W, and $\Delta U$

$\Delta U$ (Change in Internal Energy):
+ $\Delta U$ : System's internal energy increases (e.g., temperature rises).
- $\Delta U$ : System's internal energy decreases (e.g., temperature falls).
$Q$ (Energy Transferred via Heating):
+ $Q$ : Heat energy is transferred into the system (system gets hotter).
- $Q$ : Heat energy is transferred away from the system (system cools down).
$W$ (Work Done):
+ $W$ : Work is done on the system (e.g., a gas is compressed, energy input).
- $W$ : Work is done by the system (e.g., a gas expands, energy output).

The First Law in Specific Processes

The First Law can be simplified for specific types of thermodynamic processes:

Isovolumetric (or Isochoric) Process: The volume of the system remains constant ( $\Delta V = 0$ ). Since no volume change occurs, no work is done ( $W = 0$ ). The First Law simplifies to $\Delta U = Q$ . All heat added goes directly into increasing the internal energy.
Isothermal Process: The temperature of the system remains constant ( $\Delta T = 0$ ). For an ideal gas, internal energy depends only on temperature, so the change in internal energy is zero ( $\Delta U = 0$ ). The First Law becomes $0 = Q + W$ , or $Q = -W$ . Any heat added to the system is immediately converted into work done by the system.
Adiabatic Process: No heat is transferred into or out of the system ( $Q = 0$ ). This can happen if the system is perfectly insulated or if the process occurs very rapidly. The First Law simplifies to $\Delta U = W$ . If the gas expands and does work, its internal energy decreases (and it cools down). If work is done on the gas (compression), its internal energy increases (and it heats up).
Isobaric Process: The pressure of the system remains constant ( $p = \text{constant}$ ). In this case, all terms in the First Law equation ( $\Delta U = Q + W$ ) can be non-zero. The work done is calculated as $W = -p \Delta V$ .

Worked examples

See the formulas applied — reveal one step at a time, like the exam.

EXAMPLE 1

A gas in a cylinder absorbs 200 J of heat from its surroundings. Simultaneously, the gas expands, performing 70 J of work on the piston. Calculate the change in the internal energy of the gas.

1
Identify the system and processes: The system is the gas. It absorbs heat and expands.

EXAMPLE 2

A fixed mass of an ideal gas is held in a cylinder by a piston at a constant pressure of 2.5 x 10^5 Pa. The gas is heated, and its volume increases from 1.2 x 10^-3 m^3 to 1.9 x 10^-3 m^3. During this process, 450 J of thermal energy is supplied to the gas. Calculate the change in the internal energy of the gas.

1
Identify given values and signs:

How it all connects

The big idea sits in the middle — tap a linked idea to explore the link.

MAIN IDEAThe first law of thermodynamics

Tap a linked idea to see how it connects back to the main topic — that connection is what examiners reward.

Glossary

Try to recall each definition before you reveal it.

Quick check

Answer in your head first — then tap to check. No pressure.

Revision flashcards

Flip the card. Test yourself before the exam.

QUESTION · 1 / 15

What is internal energy (U)?

TAP OR SPACE TO FLIP

ANSWER

The total sum of the random kinetic and potential energies of all the particles within a body or system.

TAP OR SPACE TO FLIP BACK

1 / 15 · ← → space

Key takeaways

Review these before you close the topic — retrieval beats re-reading.

✓
$\Delta U$ (Change in Internal Energy):
✓
+ $\Delta U$ : System's internal energy increases (e.g., temperature rises).
✓
- $\Delta U$ : System's internal energy decreases (e.g., temperature falls).
✓
$Q$ (Energy Transferred via Heating):
✓
+ $Q$ : Heat energy is transferred into the system (system gets hotter).
✓
- $Q$ : Heat energy is transferred away from the system (system cools down).
✓
$W$ (Work Done):
✓
+ $W$ : Work is done on the system (e.g., a gas is compressed, energy input).
✓
- $W$ : Work is done by the system (e.g., a gas expands, energy output).

Practice — then mark it

The whole point: a real Cambridge question, marked mark-by-mark.

Real past paper[3]

9702/42 · Q3(b)(i)

With reference to molecular kinetic and potential energies, describe and explain how the internal energy of the system changes when: (i) a gas is heated at constant volume so that its temperature increases

Do it on paper → mark itMARKED MARK-BY-MARK · B1 / M1 / A1 · OFFICIAL SCHEME

Extra simulations & links

PhET, GeoGebra and other curated tools — open in a new tab.

Frequently asked

✓

Checkpoint

One marked question is worth ten re-reads — close the loop before you move on.

Checkpoint

Reading it isn’t knowing it — prove it.

Before you move on: do 9702/42 · Q3(b)(i) on paper, snap a photo, and get examiner-style feedback on exactly where you win and lose marks.

Attempt & get marked →Takes about a minute · you’ll land back on this lesson

← PREVIOUS16.1 Internal energy NEXT →17.1 Simple harmonic oscillations

The first law of thermodynamics

BY THE END, YOU CAN…

1Define internal energy and explain how it relates to temperature.
2State and apply the First Law of Thermodynamics (ΔU = Q + W).
3Interpret the signs of Q, W, and ΔU correctly in thermodynamic processes.
4Apply the First Law to isovolumetric, isothermal, and adiabatic processes.
5Calculate the work done by a gas during expansion at constant pressure (W = pΔV).

In simple terms

A friendly intro before the formal notes — no formulas yet.

The first law of thermodynamics

Cambridge 9702 Paper 4 — The first law of thermodynamics (16.2). Senpai Corner diagram-backed pilot with premium structure and live visuals.

1
$\Delta U$ (Change in Internal Energy):
2
+ $\Delta U$ : System's internal energy increases (e.g., temperature rises).
3
- $\Delta U$ : System's internal energy decreases (e.g., temperature falls).
4
$Q$ (Energy Transferred via Heating):

What this topic covers

The official Cambridge syllabus points this lesson works through.

16.2.1
Recall and use $W = pΔV$ for the work done when the volume of a gas changes at constant pressure and understand the difference between the work done by the gas and the work done on the gas
16.2.2
Recall and use the first law of thermodynamics $ΔU = q + W$ expressed in terms of the increase in internal energy, the heating of the system (energy transferred to the system by heating) and the work done on the system

Explore the concept

Use the live diagram and synced steps — play it or tap a step card to walk through.

Key formulas

Tap any symbol to reveal exactly what it means and its units.

$Work_{by} = p \Delta V$

Tap a symbol — great for exam definitions

$\Delta U = Q + W$

Tap a symbol — great for exam definitions

Full topic notes

Formal explanation with the rigour you need for the exam.

What is Internal Energy (U)?

Temperature and Internal Energy

Work Done on or by a Gas (W)

For a process occurring at a constant pressure $p$ , the work done by the gas as it expands by a volume $\Delta V$ is given by:

Work_{by} = p $\Delta V$

It's crucial to relate this to the term $W$ in the First Law equation, $\Delta U = Q + W$ . In the Cambridge A-Level Physics syllabus, $W$ represents the work done on the system. Therefore:

When a gas expands ( $\Delta V > 0$ ), it does positive work on the surroundings. The work done on the gas is negative: $W = -p \Delta V$ .
When a gas is compressed ( $\Delta V < 0$ ), the surroundings do positive work on the gas. The work done on the gas is positive: $W = -p \Delta V$ (since $\Delta V$ is negative, $W$ becomes positive).

Introducing the First Law of Thermodynamics

$\Delta U = Q + W$

Deciphering the Signs: Q, W, and $\Delta U$

$\Delta U$ (Change in Internal Energy):
+ $\Delta U$ : System's internal energy increases (e.g., temperature rises).
- $\Delta U$ : System's internal energy decreases (e.g., temperature falls).
$Q$ (Energy Transferred via Heating):
+ $Q$ : Heat energy is transferred into the system (system gets hotter).
- $Q$ : Heat energy is transferred away from the system (system cools down).
$W$ (Work Done):
+ $W$ : Work is done on the system (e.g., a gas is compressed, energy input).
- $W$ : Work is done by the system (e.g., a gas expands, energy output).

The First Law in Specific Processes

The First Law can be simplified for specific types of thermodynamic processes:

Isovolumetric (or Isochoric) Process: The volume of the system remains constant ( $\Delta V = 0$ ). Since no volume change occurs, no work is done ( $W = 0$ ). The First Law simplifies to $\Delta U = Q$ . All heat added goes directly into increasing the internal energy.
Isothermal Process: The temperature of the system remains constant ( $\Delta T = 0$ ). For an ideal gas, internal energy depends only on temperature, so the change in internal energy is zero ( $\Delta U = 0$ ). The First Law becomes $0 = Q + W$ , or $Q = -W$ . Any heat added to the system is immediately converted into work done by the system.
Adiabatic Process: No heat is transferred into or out of the system ( $Q = 0$ ). This can happen if the system is perfectly insulated or if the process occurs very rapidly. The First Law simplifies to $\Delta U = W$ . If the gas expands and does work, its internal energy decreases (and it cools down). If work is done on the gas (compression), its internal energy increases (and it heats up).
Isobaric Process: The pressure of the system remains constant ( $p = \text{constant}$ ). In this case, all terms in the First Law equation ( $\Delta U = Q + W$ ) can be non-zero. The work done is calculated as $W = -p \Delta V$ .

Worked examples

See the formulas applied — reveal one step at a time, like the exam.

EXAMPLE 1

A gas in a cylinder absorbs 200 J of heat from its surroundings. Simultaneously, the gas expands, performing 70 J of work on the piston. Calculate the change in the internal energy of the gas.

1
Identify the system and processes: The system is the gas. It absorbs heat and expands.

EXAMPLE 2

1
Identify given values and signs:

How it all connects

The big idea sits in the middle — tap a linked idea to explore the link.

MAIN IDEAThe first law of thermodynamics

Tap a linked idea to see how it connects back to the main topic — that connection is what examiners reward.

Glossary

Try to recall each definition before you reveal it.

Quick check

Answer in your head first — then tap to check. No pressure.

Revision flashcards

Flip the card. Test yourself before the exam.

QUESTION · 1 / 15

What is internal energy (U)?

TAP OR SPACE TO FLIP

ANSWER

The total sum of the random kinetic and potential energies of all the particles within a body or system.

TAP OR SPACE TO FLIP BACK

1 / 15 · ← → space

Key takeaways

Review these before you close the topic — retrieval beats re-reading.

✓
$\Delta U$ (Change in Internal Energy):
✓
+ $\Delta U$ : System's internal energy increases (e.g., temperature rises).
✓
- $\Delta U$ : System's internal energy decreases (e.g., temperature falls).
✓
$Q$ (Energy Transferred via Heating):
✓
+ $Q$ : Heat energy is transferred into the system (system gets hotter).
✓
- $Q$ : Heat energy is transferred away from the system (system cools down).
✓
$W$ (Work Done):
✓
+ $W$ : Work is done on the system (e.g., a gas is compressed, energy input).
✓
- $W$ : Work is done by the system (e.g., a gas expands, energy output).

Practice — then mark it

The whole point: a real Cambridge question, marked mark-by-mark.

Real past paper[3]

9702/42 · Q3(b)(i)

Do it on paper → mark itMARKED MARK-BY-MARK · B1 / M1 / A1 · OFFICIAL SCHEME

Extra simulations & links

PhET, GeoGebra and other curated tools — open in a new tab.

Frequently asked

✓

Checkpoint

One marked question is worth ten re-reads — close the loop before you move on.

Checkpoint

Reading it isn’t knowing it — prove it.

Before you move on: do 9702/42 · Q3(b)(i) on paper, snap a photo, and get examiner-style feedback on exactly where you win and lose marks.

Attempt & get marked →Takes about a minute · you’ll land back on this lesson

← PREVIOUS16.1 Internal energy NEXT →17.1 Simple harmonic oscillations

Revise The first law of thermodynamics for Cambridge 9702 (16.2)

In simple terms

What this topic covers

Explore the concept

Key formulas

Full topic notes

What is Internal Energy (U)?

Temperature and Internal Energy

Work Done on or by a Gas (W)

Introducing the First Law of Thermodynamics

Deciphering the Signs: Q, W, and \(\Delta U\)

The First Law in Specific Processes

Worked examples

How it all connects

Glossary

Quick check

Revision flashcards

Key takeaways

Practice — then mark it

9702/42 · Q3(b)(i)

Extra simulations & links

Frequently asked

Checkpoint

Reading it isn’t knowing it — prove it.

In simple terms

What this topic covers

Explore the concept

Key formulas

Full topic notes

What is Internal Energy (U)?

Temperature and Internal Energy

Work Done on or by a Gas (W)

Introducing the First Law of Thermodynamics

Deciphering the Signs: Q, W, and \(\Delta U\)

The First Law in Specific Processes

Worked examples

How it all connects

Glossary

Quick check

Revision flashcards

Key takeaways

Practice — then mark it

9702/42 · Q3(b)(i)

Extra simulations & links

Frequently asked

Checkpoint

Reading it isn’t knowing it — prove it.

Discuss The first law of thermodynamics