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Work at constant pressure

When a gas expands against a constant pressure, for example under a piston, the work can be written simply as the pressure times the volume change. Combined with the ideal gas law, this work can also be expressed directly from the temperature change, without computing the volume.

W=p ΔVW = p\,\Delta Vwork at constant pressure
W=nR ΔTW = nR\,\Delta Tthe same work, from the ideal gas law

Symbols

pppressure (constant)Pa
ΔV\Delta Vvolume changem³
ΔT\Delta Ttemperature changeK

Example

2 mol of gas is heated from 300300 K to 450450 K at constant pressure. W=nR ΔT=2⋅8.314⋅150≈2494W = nR\,\Delta T = 2\cdot 8.314\cdot 150 \approx 2494 J ≈2.49\approx 2.49 kJ.

W=nR ΔTW = nR\,\Delta T is a shortcut that avoids computing the volumes before and after separately.
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