Question

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

Answer 1

Answer on Question #66527-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 equation of state for ideal gas:

$$p = \frac {\nu R T}{V}.$$

Thus,

$$W = \int_ {V _ {1}} ^ {V _ {2}} p d V = \int_ {V _ {1}} ^ {V _ {2}} \frac {\nu R T}{V} d V = \nu R T \int_ {V _ {1}} ^ {V _ {2}} \frac {1}{V} d V = \nu R T \ln \frac {V _ {2}}{V _ {1}}$$

An expression for the work done by a gaseous system for an isothermal expansion of an ideal gas is

$$W = \nu R T \ln \frac {V _ {2}}{V _ {1}} = p _ {1} V _ {1} \ln \frac {V _ {2}}{V _ {1}}$$

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