Question

6. Consider an ideal gas that undergoes isothermal (constant temperature) expansion from state “1” to state “2” along two different paths: a) reversibly and b) irreversibly. For these two paths, compare the relative magnitude (i.e. greater/same/lower) of the expansion work that ideal gas does to the surroundings. Make sure to justify your answer (suggestion to use a P-V diagram).

Answer 1

The work is done by/on the gas in an isothermal reversible expansion is as follows.

W = - nRT ln (V2/V1)

Where as the work done in the isothermal irreversible process is as follows.

W = P (V2-V1)

In general, the work done by the gas in the isothermal reversible process is greater than in the work done in the irreversible process. This is because in the reversible process the work done is equals to the summation of individual work done by infinitesimally small steps. So it is greater than the irreversible process in magnitude.