# Isothermal Reversible Expansion

An isothermal process is a process which is conducted in a manner such that the temperature remains constant during the entire operation.

Consider an ideal gas confined in a cylinder with a frictionless piston.

Suppose it expands reversibly from volume at a constant temperature, the pressure of the gas is successfully reduced from .

The reversibly expansion of the gas takes place in a finite number of infinitesimally small intermediate steps. To start with the external pressure, is arranged equal to the internal pressure of the gas and the piston remains stationary.

If is decreased by an infinitesimal amount dP the gas expands reversibly and the piston moves through a distance dl.

Since dP is so small, for all practical purposes hence,

The work done by gas in one infinitesimal step (dw), can be expressed as:

(A = cross-section area of piston)

where dV is the increase in volume. The total amount of work done by the isothermal reversible expansion of the ideal gas from is, therefore,

…..(vii)

By the ideal gas equation,

On integration, we get

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