Internal energy (AQA A-Level Physics): Revision Notes
Internal energy
What is internal energy?
When we think about the energy stored in any object or substance, we need to consider the particles that make it up. These particles are constantly moving in random directions, vibrating, rotating, and exerting forces on each other. All this activity represents energy stored within the substance.
Internal energy is the total energy stored within a system due to the random motion and positions of its particles. More precisely, it is the sum of the randomly distributed kinetic energy and the potential energy of all particles in a body.
The kinetic energy component comes from the translational, rotational, and vibrational motion of the particles. The potential energy component arises from the attractive forces between particles - when particles are separated against these forces, they gain potential energy.
Changing internal energy
There are two distinct ways to increase the internal energy of a system: by heating and by doing work on the system. Although both methods increase internal energy, they differ in how the energy is transferred.
Heating
Heating refers to an energy transfer caused by a temperature difference. This type of energy transfer is called a thermal energy transfer.
Example: Heating a Metal Nail
When you place a metal nail in contact with a flame from a Bunsen burner, energy transfers from the hotter flame to the cooler nail. This thermal energy transfer increases the internal energy of the nail, causing its temperature to rise.
Doing work
Doing work involves an energy transfer that occurs as a result of a force moving through a distance.
Example: Hammering a Metal Nail
If you repeatedly strike a metal nail with a hammer, you perform work on the nail. Each impact transfers energy to the nail, increasing its internal energy. Just like heating the nail, this also causes the temperature of the nail to rise.
Both methods achieve the same result - an increase in the internal energy and temperature of the nail - but through different energy transfer mechanisms.
Systems doing work
In some situations, a system can do work on its surroundings, which decreases its internal energy. Consider carbon dioxide gas contained at high pressure in a cylinder. When the gas is allowed to escape, it expands rapidly and pushes back against the atmosphere, doing work on its surroundings.
This work is done at the expense of the gas's internal energy. The cooling can be so significant that some of the carbon dioxide solidifies to form solid carbon dioxide, commonly known as dry ice.
The equivalence of heat and work
During the 19th century, scientist James Prescott Joule, a brewer from Salford near Manchester, conducted experiments that established the equivalence between heat and work. In his famous paddle wheel experiment, Joule demonstrated that doing mechanical work on a liquid by rotating paddles raised the liquid's temperature by exactly the same amount as applying heat to the liquid would have done.
Joule's Key Discovery
Joule's careful measurements determined the precise amounts of mechanical work and heat needed to raise the temperature of a specific mass of water by the same amount. This groundbreaking work established that heat and work are equivalent forms of energy transfer, which is why both quantities are measured in the same unit: the joule.
The first law of thermodynamics
The equivalence of heating and work in affecting internal energy is formalized in the first law of thermodynamics. This law represents a statement of energy conservation for thermal systems.
The First Law of Thermodynamics
The first law can be expressed in two complementary ways:
For increasing internal energy: The increase in internal energy of a system equals the sum of the energy transferred to the system by heating and the energy transferred to the system by work done on it by an external force.
For decreasing internal energy: The decrease in internal energy of a system equals the sum of the energy transferred away from the system by cooling and the energy transferred away from the system as a result of the system doing work against an external force.
These statements tell us that the total change in internal energy depends only on the net energy transferred to or from the system, regardless of whether that transfer occurs through heating, cooling, or work.
Internal energy and temperature
The kinetic component of internal energy is directly related to a body's temperature. When energy is transferred to a substance by heat or work and results in a temperature rise, this indicates that the kinetic energy of the particles has increased. The particles are now moving faster on average.
However, if expansion or a change of state occurs (such as melting or vaporization), this indicates an increase in the potential energy component of the substance's internal energy. During these processes, energy goes into separating particles against their mutual attractive forces, rather than increasing their speed. This is why the temperature may remain constant during a change of state even though energy is being transferred to the substance.
Key Points to Remember:
- Internal energy is the sum of the randomly distributed kinetic energy and potential energy of all particles in a body
- There are two ways to change internal energy: heating (energy transfer due to temperature difference) and doing work (energy transfer due to force moving)
- Heat and work are equivalent - both can increase internal energy by the same amount, which is why they share the same unit (joules)
- The first law of thermodynamics states that the change in internal energy equals the net energy transferred by heating plus the net work done on the system
- The kinetic component of internal energy relates to temperature, while the potential energy component changes during expansion or changes of state