Physics 001.001.016 Internal Energy in a System
Alignment
Learning Intentions
By the end of the lesson, students will be able to:
- Explain the first law of thermodynamics as a statement of energy conservation.
- Describe how heating and work can change the internal energy of a system.
- Apply the relationship
using the correct sign convention. - Distinguish between work done on a system and work done by a system.
Success Criteria
By the end of the lesson, students have successfully:
- Defined internal energy as the total microscopic kinetic and potential energy of particles in a system.
- Identified whether energy is added to or removed from a system by heating.
- Identified whether work is done on or by the system.
- Used
to calculate the change in internal energy. - Explained that the first law of thermodynamics is a consequence of the law of conservation of energy.
Syllabus Reference
- Unit 1: Thermal, Nuclear and Electrical Physics
- Topic 1: Heating Processes
- Phase Changes and Energy Conservation
- Explain that the change in the internal energy of a system is equal to the energy added or removed by heating plus the work done on or by the system, and recognise this as the first law of thermodynamics and that this is a consequence of the law of conservation of energy.
Phenomenon
A bicycle pump becomes warm when air is compressed quickly.
When the handle of the pump is pushed down, work is done on the air inside the pump. The air molecules move faster on average, so the internal energy of the air increases. Some of this increased internal energy is then transferred as heat to the metal pump and the surroundings, making the pump feel warm.
This phenomenon shows that the internal energy of a system can change because:
- energy is transferred by heating
- work is done on or by the system
Key Idea
The first law of thermodynamics states that the change in the internal energy of a system is equal to the energy transferred by heating plus the work done on the system.
This is a statement of the law of conservation of energy: energy cannot be created or destroyed, only transferred or transformed.
Concept
The internal energy of a system can increase or decrease when energy crosses the system boundary.
There are two main ways this can happen in thermodynamics:
-
Heating Energy is transferred because of a temperature difference.
-
Work Energy is transferred when a force causes displacement, such as gas expanding, gas being compressed, or a piston moving.
For the sign convention used in this lesson:
| Quantity | Positive when | Negative when |
|---|---|---|
| heat is added to the system | heat is removed from the system | |
| work is done on the system | work is done by the system | |
| internal energy increases | internal energy decreases |
Therefore:
Where:
If work is done by the system (or loses something), then
Convention
In this lesson, the system is the object(s) or material(s) being studied.
Examples:
| Situation | System | Surroundings |
|---|---|---|
| Gas in a syringe | gas | syringe, hand, air outside |
| Water in a kettle | water | kettle element, kettle, air |
| Steam engine cylinder | steam | piston, cylinder, external load |
The system boundary separates the system from the surroundings.
Energy entering the system is positive.
Energy leaving the system is negative.
The first law can also be written as:
where
This is equivalent to:
when
Misconceptions
Common misconceptions students have regarding the concept when applying to various situations and solving problems. It could be a conceptual, mathematical or logical misconception.
- Students may think heat and temperature are the same thing. Heat is energy transferred due to a temperature difference, while temperature is related to the average kinetic energy of particles.
- Students may think internal energy only means temperature. Internal energy includes microscopic kinetic and potential energy of particles.
- Students may forget that work done by the system is negative when using
. - Students may think energy is “used up” or destroyed. The first law states that energy is conserved, even when it becomes less useful.
- Students may assume
in all cases, ignoring work done on or by the system.
Further Reading
- QCAA Physics 2025 v1.2 General Senior Syllabus: Unit 1, Heating Processes
- Heat engines and the development of steam engines
- Conservation of energy in mechanical and thermal systems
- Thermodynamics in internal combustion engines and refrigerators
Explicit Instruction
Begin by asking students:
A sealed gas cylinder is heated while the gas also expands and pushes a piston outward. Does all the heating energy stay inside the gas?
Expected response:
No. Some energy increases the internal energy of the gas, while some energy is transferred out of the gas as mechanical work on the piston.
Introduce the first law:
Explain each part:
If
If
If
If
If
If
If
The first law does not describe a new type of energy. It is a bookkeeping rule for energy transfers.
Energy added to the system either:
- increases internal energy
- leaves again as work done by the system
- or both
Worked Examples
Worked Example 1
A gas in a sealed container is heated. The gas receives
Given:
Using:
Substitute:
Answer:
The internal energy of the gas increases by
Explanation:
Because the container is rigid, the gas cannot expand and do work. All the energy transferred by heating increases the internal energy of the gas.
Worked Example 2
A gas is compressed in a bicycle pump. During compression,
Given:
Using:
Substitute:
Answer:
The internal energy of the gas increases by
Explanation:
Work done on the gas increases its internal energy, but some energy leaves the gas by heating. The net effect is an increase of
Worked Example 3
A gas in a cylinder is heated by
Given:
The gas does work on the piston, so work is done by the system.
Therefore:
Using:
Substitute:
Answer:
The internal energy of the gas increases by
Explanation:
Although
Check for Understanding
Check 1
A system gains
Answer:
The internal energy increases by
Check 2
A gas has
Answer:
The internal energy increases by
Check 3
A gas receives
Answer:
The internal energy does not change.
This means the energy added by heating is transferred out as work.
Investigation (Alternative to Explicit)
Hypothesis
If work is done on a gas by compression, then the internal energy of the gas will increase, causing a measurable temperature increase.
Data Collection
Teacher demonstration:
Use a bicycle pump, temperature probe, and pressure-safe setup.
Method:
- Measure the initial temperature of the air near the pump outlet.
- Compress the pump quickly several times.
- Measure the temperature of the pump barrel or air near the outlet.
- Allow the pump to cool.
- Repeat with slower compressions.
- Compare the observed temperature change.
Safety:
- Do not block the pump outlet completely unless the apparatus is designed for this.
- Keep fingers clear of moving parts.
- Avoid excessive compression that may damage equipment.
Analysis
Students identify the system as the air inside the pump.
During compression:
- work is done on the air
- internal energy increases
- temperature increases
- some energy is transferred to the surroundings by heating
Using the first law:
For fast compression:
is positive may be slightly negative because heat leaves the air is positive overall
Evaluation
Students discuss:
- Why the pump becomes warmer
- Whether all work done on the air remains as internal energy
- Why some energy is transferred to the surroundings
- Sources of uncertainty in measuring temperature
- Whether the system was perfectly isolated
Problems
The following problems are designed to develop fluency with the first law of thermodynamics and the sign convention for heating and work.
-
A gas receives
of energy by heating. No work is done. Calculate . -
A gas loses
of energy by heating. No work is done. Calculate . -
A gas has
of work done on it and receives of energy by heating. Calculate . -
A gas receives
of energy by heating and does of work on the surroundings. Calculate . -
A system loses
by heating and has of work done on it. Calculate . -
A gas expands and does
of work on a piston. At the same time, of energy is added by heating. Calculate and explain the result. -
A system’s internal energy increases by
when of energy is added by heating. How much work was done by the system? -
A system’s internal energy decreases by
while of work is done by the system. How much energy was transferred by heating? -
A gas is compressed so that
of work is done on it. Its internal energy increases by . How much energy was transferred by heating, and did heat enter or leave the gas? -
A heat engine absorbs
of energy by heating and does of work on the surroundings. Calculate the change in internal energy of the working gas.
Answers:
-
-
-
-
-
-
The energy added by heating is transferred out as work, so internal energy does not change.
Since
Work is done by the system, so:
Energy was added to the system by heating.
The gas does work on the surroundings, so:
Followup
Self-check
Students should be able to answer:
- What does internal energy mean?
- What is the first law of thermodynamics?
- Why is the first law a consequence of conservation of energy?
- What does it mean if
is positive? - What does it mean if
is negative? - What does it mean if
is positive? - What does it mean if
is negative? - Why does compressing a gas usually increase its temperature?
- Why can a gas do work on a piston?
- Why is the sign convention important when solving first law problems?
Next Topic
Efficiency of heat transfers.
Students will use:
and connect this to the idea that energy is conserved, but not all energy remains useful after a transfer or transformation.