1. What Is Work in Thermodynamics?
In thermodynamics, work is the energy transferred when a force moves the boundary of a system. For gases, this usually means the movement of a piston as the gas expands or gets compressed.
If the gas pushes the piston outward, the system does work. If the piston pushes the gas inward, work is done on the system.
2. Mathematical Expression for Work
For a gas at pressure \( P \) expanding or contracting by a small change in volume \( dV \), the work is:
\( dW = P \, dV \)
2.1. Meaning of the Sign
- If \( dV > 0 \) (expansion), work done by the gas is positive.
- If \( dV < 0 \) (compression), work done by the gas is negative.
2.2. Total Work
To find total work from an initial volume \( V_1 \) to final volume \( V_2 \):
\( W = \int_{V_1}^{V_2} P \, dV \)
This is the area under the P–V curve.
3. Work Done During Expansion
When a gas expands, it pushes against the external pressure, moving a boundary. This requires energy, so the gas does positive work on the surroundings.
3.1. Example
When air in a heated cylinder expands, the piston moves outward and the gas performs work using its internal energy.
4. Work Done During Compression
When the gas is compressed, the surroundings do work on the gas. The volume decreases and energy is added to the system.
4.1. Example
When air is pumped into a tyre, the piston compresses the air. The work done on the air increases its internal energy, making it warmer.
5. Work in Different Thermodynamic Processes
The amount of work depends on how pressure and volume change. Each thermodynamic process has its own pattern of work done.
5.1. Isothermal Process
Temperature remains constant. Work done depends on how pressure changes with volume:
\( W = nRT \ln \left( \dfrac{V_2}{V_1} \right) \)
5.2. Adiabatic Process
No heat exchange. Work is related to pressure and volume by:
\( PV^\gamma = \text{constant} \)
5.3. Isobaric Process
Pressure remains constant. Work is simply:
\( W = P (V_2 - V_1) \)
5.4. Isochoric Process
Volume remains constant (\( dV = 0 \)). No work is done.
6. Interpreting Work from a P–V Diagram
A P–V diagram visually shows how work changes in a process. The work done is the area under the curve between initial and final volumes.
6.1. Expansion Curve vs Compression Curve
An expansion curve moves toward larger volumes; a compression curve moves toward smaller volumes. The area under each gives the corresponding work.
6.2. Closed Cycles
For cyclic processes like heat engines, the work done is the area enclosed by the loop on the P–V diagram.
7. Everyday Examples of Work in Thermodynamics
- An internal combustion engine uses expanding gases to push pistons and do work.
- A bicycle pump warms up because work done on the air increases internal energy.
- Steam pushing a turbine blade in a power plant is another example of work by expanding gas.