Internal Energy, Heat and Work
1. Internal Energy (U)
Internal energy is the total microscopic energy possessed by a thermodynamic system.
Definition
It is the sum of:
- Kinetic Energy of molecules due to:
- Translational motion
- Rotational motion
- Vibrational motion
- Potential Energy due to intermolecular forces between molecules.
Therefore,
U = Total Molecular Kinetic Energy + Total Molecular Potential Energy
Important Points
- Internal energy includes only the random microscopic motion of molecules.
- It does not include the kinetic energy of the entire system moving as a whole.
- It is measured in a frame where the centre of mass of the system is at rest.
Example:
A gas inside a cylinder possesses internal energy due to molecular motion.
If the cylinder is thrown upward, the kinetic energy of the moving cylinder is not part of its internal energy.
State Variable
Internal energy is a state function (state variable).
Its value depends only on the present state of the system:
$$ U = f(P,V,T) $$
where:
- P = Pressure
- V = Volume
- T = Temperature
It does not depend on the path followed to reach that state.
2. Heat (Q)
Heat is a mode of energy transfer.
Definition
Heat is the energy transferred between a system and its surroundings due solely to a temperature difference.
Energy always flows:
$$ \text{Higher Temperature} \rightarrow \text{Lower Temperature} $$
until thermal equilibrium is reached.
Characteristics
- Heat is not stored in a system.
- Heat exists only during energy transfer.
- Symbol: Q
- Unit: Joule (J)
Example:
When a gas cylinder is placed on a flame, energy enters the gas as heat.
3. Work (W)
Work is another mode of energy transfer.
Definition
Work is the energy transferred by mechanical means without requiring a temperature difference.
Characteristics
- Work is not a property of the system.
- Work exists only while energy is being transferred.
- Symbol: W
- Unit: Joule (J)
Example:
When a piston is pushed downward, the gas is compressed and energy enters the gas as mechanical work.
4. Difference Between Internal Energy, Heat and Work
Internal Energy
- Energy possessed by the system.
- A state variable.
- Stored within the system.
Heat
- Energy crossing the system boundary due to temperature difference.
- Path dependent.
- Cannot be stored.
Work
- Energy crossing the system boundary through mechanical interaction.
- Path dependent.
- Cannot be stored.
5. Energy in Transit Concept
A common mistake is to think that a system contains heat or work.
In thermodynamics:
Incorrect Statements
- A gas contains heat.
- A gas possesses work.
Correct Statements
- A gas possesses internal energy.
- Heat is supplied to the gas.
- Work is done on the gas.
- Work is done by the gas.
Key Idea
Heat and work are simply energy in transit.
Once energy enters the system, it becomes part of the internal energy.
$$ \text{Heat} \rightarrow U $$
$$ \text{Work} \rightarrow U $$
Thus, a system contains only internal energy, not heat or work.
6. Methods of Changing Internal Energy
The internal energy of a gas can be changed in two ways.
(A) By Heating or Cooling
When heat is supplied:
$$ Q > 0 $$
Internal energy increases.
When heat is removed:
$$ Q < 0 $$
Internal energy decreases.
Example:
Heating a gas cylinder with a flame increases its internal energy.
(B) By Doing Work
When work is done on the gas:
$$ W > 0 $$
Internal energy increases.
Example:
Compressing a gas by pushing a piston downward.
When the gas does work on the surroundings:
$$ W < 0 $$
Internal energy decreases.
Example:
Expansion of gas pushing the piston upward.
7. Summary
- Internal energy is the total microscopic energy of molecules.
- Internal energy is a state variable.
- Heat and work are not stored energies.
- Heat is energy transfer due to temperature difference.
- Work is energy transfer through mechanical means.
- Heat and work are called energy in transit.
- Internal energy can be changed by:
- Heat transfer
- Work transfer
- Energy entering the system as heat or work ultimately becomes part of the system's internal energy.
Frequently Asked Questions (FAQ)
Q1. What is internal energy?
Internal energy is the sum of all microscopic kinetic and potential energies of molecules in a system.
Q2. Is internal energy a state function?
Yes. Internal energy depends only on the current state of the system.
Q3. Can a system contain heat?
No. Heat is only energy in transit due to temperature difference.
Q4. Can a system contain work?
No. Work is only energy transferred through mechanical interaction.
Q5. What are the two methods of changing internal energy?
Heat transfer and work transfer.
Quiz
1. Internal energy includes:
- A. Only kinetic energy
- B. Only potential energy
- C. Both molecular kinetic and potential energies
- D. Gravitational energy
Answer: C. Both molecular kinetic and potential energies
2. Heat is transferred due to:
- A. Pressure difference
- B. Volume difference
- C. Temperature difference
- D. Density difference
Answer: C. Temperature difference
3. Internal energy is a:
- A. Path function
- B. State function
- C. Vector quantity
- D. Conserved force
Answer: B. State function
4. Which of the following is energy in transit?
- A. Internal Energy
- B. Temperature
- C. Heat and Work
- D. Pressure
Answer: C. Heat and Work
5. Compressing a gas by pushing a piston downward:
- A. Decreases internal energy
- B. Increases internal energy
- C. Keeps internal energy constant
- D. Makes temperature zero
Answer: B. Increases internal energy
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