The assertion in an adiabatic system is that the change in internal energy of a gas is equal to the work done on or by the gas in the process.
An adiabatic process is a fundamental thermodynamic process characterized by the absence of heat transfer between the system (e.g., a gas) and its surroundings. This means that the system is perfectly insulated, preventing any exchange of thermal energy.
Understanding the Adiabatic Assertion
This assertion is a direct consequence of the First Law of Thermodynamics, which is a statement of energy conservation. The First Law states that the change in a system's internal energy ($\Delta U$) is equal to the heat added to the system ($Q$) minus the work done by the system ($W$):
$\Delta U = Q - W$
In an adiabatic process, the defining condition is that no heat is exchanged with the surroundings, meaning $Q = 0$. Substituting this into the First Law equation simplifies it to:
$\Delta U = -W$
This simplified equation reveals the core of the assertion:
- Work Done by the Gas: If the gas expands and performs work by the system ($W$ is positive), its internal energy decreases ($\Delta U$ is negative). This often leads to a drop in the gas's temperature.
- Work Done on the Gas: If work is done on the system (e.g., the gas is compressed), $W$ is negative (representing work done on the system rather than by it). In this case, $\Delta U = -(-W{on}) = W{on}$, meaning the internal energy of the gas increases, typically leading to a rise in its temperature.
Therefore, the entire change in the internal energy of the system during an adiabatic process is solely due to the work done on or by the system.
Key Characteristics of Adiabatic Processes:
- No Heat Transfer (Q=0): This is the defining condition, indicating perfect thermal insulation or extremely rapid processes.
- Temperature Changes: Unlike isothermal processes where temperature remains constant, the temperature of the gas does change in an adiabatic process. Compression causes temperature to rise, while expansion causes it to fall. This is because the work directly alters the internal energy, which is linked to temperature.
- Real-World Approximations: While perfectly adiabatic processes are ideal, many rapid processes in nature or engineering can be approximated as adiabatic because there isn't sufficient time for significant heat transfer to occur. Examples include the compression stroke in an internal combustion engine or the propagation of sound waves in a medium.
