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Question
Answer the following in one or two sentences.
Comment on the statement:
no work is involved in an expansion of gas in a vacuum.
Solution
- A free expansion means expansion against zero opposing force. Such expansion occurs in a vacuum.
- When the gas expands in a vacuum, there is no opposing force, that is, Pext = 0. The work done by a system during such expansion is
W = - Pext Δ V = 0
Thus, no work is done when the gas expands freely in a vacuum.
Note: Units of energy and work:
1 J = 1 kg m2 s-2 = 1 Pa m3
1 Pa = 1 kg m-1 s-2
From the equation, W = – Pext∆V
If the pressure is expressed in bar and ΔV in dm3, then the work has the units of bar dm3.
1 bar = 105 Pa = 105 kg m–1 s–2
1 dm3 bar = dm3 × 105 kg m-1 s-2
= m3 × 10-3 × 105 kg m-1 s-2
= 100 kg m2 s-2 = 100 J
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