## Question

###### A sample of an ideal gas in a cylinder of volume 2.82 L at 298 K...

A sample of an ideal gas in a cylinder of volume 2.82 L at 298 K and 2.63 atm expands to 8.40 L by two different pathways. Path A is an isothermal, reversible expansion. Path B has two steps. In the first step, the gas is cooled at constant volume to 1.40 atm, In the second step, the gas is heated and allowed to expand against a constant external pressure of 1.40 atm until the final volume is 8.40L. Calculate the work for path A. Calculate the work for path B. LU

## Answers

Path A:

Work done in isothermal process = nRT* ln(V

_{i}/ V_{f}), where n is number of moles, V_{i}is initail volume and V_{f}is final volumeFrom ideal gas equation: pV = nRT. Using this we get: w = PV * ln(V

_{i}/ V_{f})Using the given values: 2.63 * 2.82 * ln(2.82 / 8.40) = -8.095 lit-atm = -8.095 * 101.325 = -820.23 J

Path B:

Work done = -P * Change in Volume = -1.40 * (8.40 - 2.82) = -7.812 lit-atm = -791.55 J

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