Topic 8.48 min read
First Law of Thermodynamics
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.
Choose Your Level
Beginner Level
Energy given to a system as heat has two possible uses: it can increase the system’s internal energy, and it can allow the system to do work on its surroundings.
Recommended for Class 11
First Law of Thermodynamics
Overview
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.
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.
ΔU = −200 J and W = +50 J
Q = ΔU + W
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.
- Test me with an MCQ.
Exam Focus
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.
Important formulas
- Q = ΔU + W
- ΔU = Q − W
- ΔU = U₂ − U₁
Common exam traps
- 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.
Long question structure
Definition → condition → first-law reduction → graph → physical explanation → example.
Common Mistakes
Common Mistakes
- Mistake
Use one sign convention consistently; these notes use work done by the system as positive.
- Mistake
A decrease in internal energy means ΔU is negative.
- Mistake
A negative Q means heat leaves the system.
- Mistake
Do not assume all supplied heat becomes work.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
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.
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.
- Definition
- 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.
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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?
Important Question
Q4. What does Q < 0 mean?