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(Vi / Vf), where n is number of moles, Vi is initail volume and Vf is final volume
From ideal gas equation: pV = nRT. Using this we get: w = PV * ln(Vi / Vf)
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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