The first law of thermodynamics applies conservation of energy to a system: heat supplied equals the increase in internal energy plus work done by the system.
Learning Outcomes
The first law is the law of conservation of energy applied to thermodynamics.
Using the textbook convention, Q = ΔU + W.
Q is positive when heat enters the system and negative when heat leaves.
W is positive for expansion work done by the system and negative for compression.
ΔU = U₂ − U₁ depends only on initial and final states, not the path.
Equivalent form: ΔU = Q − W.
Intermediate Level
Statement
Whenever heat Q is added to a system, part may raise its internal energy and part may leave as mechanical work done on the surroundings. Energy is transformed, not created or destroyed.
Key equation
Q=Δ U+W
Key equation
Δ U=Q-W
Key equation
Δ U=U2-U1
Textbook Sign Convention
Quantity
Positive
Negative
Q
heat enters system
heat leaves system
W
system expands and does work
surroundings compress gas and do work on it
ΔU
internal energy increases
internal energy decreases
Internal Energy Is a State Function
The value of ΔU is fixed by the initial and final states. Heat Q and work W depend on the path followed, but their difference Q − W must give the same ΔU for the same endpoints.
Everyday Applications
Melting ice absorbs heat and changes the system’s energy.
A pump transfers mechanical work to air in a tyre, raising its internal energy.
Food supplies energy used by the body for work and maintaining internal energy.
Heat Rejected by a Gas
The internal energy of a gas decreases by 200 J while the gas does 50 J of work. Find Q.
1
Working
ΔU = −200 J and W = +50 J
2
Step 2
Q = ΔU + W
3
Step 3
Q = −200 J + 50 J
Final answer:Q = −150 J
Common Mistakes
Use one sign convention consistently; these notes use work done by the system as positive.
A decrease in internal energy means ΔU is negative.
A negative Q means heat leaves the system.
Do not assume all supplied heat becomes work.
Short-Question Preparation
Q. State the first law of thermodynamics.
A. Heat supplied equals the increase in internal energy plus work done by the system: Q = ΔU + W.
Q. What is the equivalent equation for ΔU?
A.ΔU = Q − W.
Q. Why is internal energy called a state function?
A. Its change depends only on the initial and final states, not on the path.
Q. What does Q < 0 mean?
A. Heat is transferred from the system to the surroundings.
Sticky Notes
The first law is the law of conservation of energy applied to thermodynamics.
Using the textbook convention, Q = ΔU + W.
Q is positive when heat enters the system and negative when heat leaves.
W is positive for expansion work done by the system and negative for compression.
ΔU = U₂ − U₁ depends only on initial and final states, not the path.
Equivalent form: ΔU = Q − W.
60-Second Revision
Use Q = ΔU + W with W positive for work done by the system. Thus ΔU = Q − W. Heat and work depend on the process path, while ΔU depends only on the initial and final states.
Summary
The first law of thermodynamics applies conservation of energy to a system: heat supplied equals the increase in internal energy plus work done by the system.
Ask-the-Tutor Modes
Explain the energy transfers simply.
Apply the textbook sign convention.
Derive the reduced equation.
Solve a numerical step by step.
Explain the P–V graph.
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Exam preparation
Exam Focus
Important points
The first law is the law of conservation of energy applied to thermodynamics.
Using the textbook convention, Q = ΔU + W.
Q is positive when heat enters the system and negative when heat leaves.
W is positive for expansion work done by the system and negative for compression.
ΔU = U₂ − U₁ depends only on initial and final states, not the path.
Equivalent form: ΔU = Q − W.
Common mistakes
Use one sign convention consistently; these notes use work done by the system as positive.
A decrease in internal energy means ΔU is negative.
A negative Q means heat leaves the system.
Do not assume all supplied heat becomes work.
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.
First Law of Thermodynamics
Sticky Notes · Quick Revision
1.
Key Point 1
The first law is the law of conservation of energy applied to thermodynamics.
2.
Key Point 2
Using the textbook convention, Q = ΔU + W.
3.
Key Point 3
Q is positive when heat enters the system and negative when heat leaves.
4.
Key Point 4
W is positive for expansion work done by the system and negative for compression.
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8 concept questions
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Explanation after each answer
Exam Practice
Important Question
Q1. State the first law of thermodynamics.
Important Question
Q2. What is the equivalent equation for ΔU?
Important Question
Q3. Why is internal energy called a state function?
