On a pressure–volume graph, an ideal gas in a cylinder fitted with a piston expands irreversibly against a constant external pressure of 2.0 bar, from 1.0 L to 6.0 L. The work is shown as the shaded rectangle under a horizontal line at 2.0 bar between these two volumes. What is the work done on the gas? (1 L bar = 100 J)
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Against a constant external pressure, w = −pex ΔV = −(2.0 bar)(6.0 − 1.0) L = −10 L bar. With 1 L bar = 100 J, w = −1000 J; the negative sign shows work is done by the gas.
- B.
During expansion the gas does work on the surroundings, so the work done on the gas is negative.
- C.
This uses the final volume 6.0 L instead of the change in volume, 5.0 L.
- D.
This omits the pressure: the area is 2.0 bar × 5.0 L = 10 L bar, not 5 L bar.
NCERT: Class 11 Chemistry, Chapter 5