Work Done in Isothermal Process

📊 intermediate

$$W = nRT \ln\left(\frac{V_2}{V_1}\right)$$

Work done by an ideal gas when temperature is held constant.

Variables & Units

$V_1, V_2$

Initial and Final Volumes

Unit: $m^3$

Key Information

📐 Derived From

Integral of $P dV$ with $P = nRT/V$.

💡 Example

Expanding gas at $300K$ to double its volume.

🔧 Applications

Heat engines and industrial compression.

⚠️ Constraints

Ideal gas; constant temperature.

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