Energy Conservation in Thermodynamics
- Thermodynamics explores how energy is transferred and transformed, particularly through heat and work.
- These concepts are governed by the first law of thermodynamics, which is a specific application of the law of conservation of energy.
The First Law of Thermodynamics: Energy Conservation
First law of thermodynamics
The first law of thermodynamics states that the total energy of an isolated system is constant.
In other words, energy can be transferred or transformed, but it cannot be created or destroyed.Note
The first law of thermodynamics is a specific application of the law of conservation of energy to thermodynamic systems.
Internal Energy, Heat, and Work
To understand how energy is conserved in thermodynamics, we need to consider three key components:
- Internal Energy ($U$): The total energy contained within a system, including the kinetic and potential energy of its particles.
- Heat ($Q$): The energy transferred between a system and its surroundings due to a temperature difference.
- Work ($W$): The energy transferred when a force acts over a distance, such as when a gas expands or is compressed.
The First Law of Thermodynamics: Mathematical Formulation
The first law of thermodynamics can be expressed mathematically as:
$$Q = \Delta U + W$$
where:
- $Q$ is the heat added to the system.
- $ΔU$ is the change in internal energy of the system.
- $W$ is the work done by the system.
The sign convention is important:
- $Q > 0$: Heat is added to the system.
- $Q< 0$: Heat is removed from the system.
- $W>0$: Work is done by the system (e.g., expansion).
- $W< 0$: Work is done on the system (e.g., compression).
How Energy is Conserved
The equation $Q = \Delta U + W$ shows that the energy added to a system as heat (Q) is used to either:
- Increase the system’s internal energy ($\Delta U$).
- Perform work ($W$) on the surroundings.
If no heat is added or removed ($Q = 0$), any work done by the system must come from its internal energy, leading to a decrease in $U$.
Example- Consider a gas in a cylinder with a piston.
- If you heat the gas, it can expand, pushing the piston outward.
- The energy you supplied as heat is used to increase the gas’s internal energy and to do work on the piston.
Work Done on or by a Gas
In thermodynamics, work is often associated with changes in the volume of a gas.
