Question

What is an isothermal process? Obtain an expression for work done by a gas in an isothermal process.

Hint:

In an isothermal process, the temperature remains constant, and the work done by the gas is determined by the logarithmic ratio of the final and initial volumes.

Answer 1

An isothermal process is one in which the temperature of the system remains unchanged (\( \Delta T = 0 \)). During this process, the internal energy of an ideal gas does not change, and the work done depends on the changes in pressure and volume. The work done by a gas in an isothermal process is expressed as: \[ W = nRT \ln \left(\frac{V_f}{V_i}\right) \] where \( n \) is the number of moles, \( R \) is the universal gas constant, \( T \) is the temperature, and \( V_i \) and \( V_f \) are the initial and final volumes. \bigskip