Work Done in Adiabatic Process

📊 advanced

$$W = \frac{P_1V_1 - P_2V_2}{\gamma - 1}$$

Calculates the work done by or on an ideal gas when no heat is exchanged with the surroundings.

Variables & Units

$P_1, V_1$

Initial Pressure and Volume

Unit: $Pa, m^3$

$P_2, V_2$

Final Pressure and Volume

Unit: $Pa, m^3$

$\gamma$

Adiabatic Index ($C_p/C_v$)

Unit: Dimensionless

Key Information

📐 Derived From

Integration of $P dV$ using the relation $PV^\gamma = \text{constant}$.

💡 Example

Work done during the compression stroke of a diesel engine.

🔧 Applications

Internal combustion engines and atmospheric physics.

⚠️ Constraints

Reversible adiabatic process; ideal gas.

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