Question

Derive an expression for the work done by a gaseous system for an isothermal expansion of an ideal gas.

Answer 1

Answer on Question #66801, Physics / Molecular Physics | Thermodynamics

Derive an expression for the work done by a gaseous system for an isothermal expansion of an ideal gas.

**Solution:**

The work done by a gaseous system for an isothermal expansion of an ideal gas:

$$W = \int_{0}^{W} dW = \int_{V_{1}}^{V_{2}} P dV = \int_{V_{1}}^{V_{2}} \frac{m}{M} \frac{RT}{V} dV = \frac{m}{M} RT \ln \frac{V_{2}}{V_{1}},$$

where $P$ is the press of gas, $m$ is the mass of gas, $M$ is the molar mass of gas, $R$ is the gas constant, $T$ is the absolute temperature of the gas, $V_{1}$ is the initial volume of gas, $V_{2}$ is the last volume of gas.

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