Helium gas expands from 125 kPa, 350 K and 0.25 m3 to 100 kPa in a pol

1.	Helium gas expands from 125 kPa, 350 K and 0.25 m3 to 100 kPa in a polytropic process with n = 1.667. Is the work positive, negative or zero?
Answer» The boundary work is: W = ⌡P dV P drops but does V go up or down? The process equation is: PVⁿ = C so we can solve for P to show it in a P-V diagram P = CV^-n as n = 1.667 the curve drops as V goes up we see V₂ > V₁ giving dV > 0 and the work is then positive.

Helium gas expands from 125 kPa, 350 K and 0.25 m3 to 100 kPa in a polytropic process with n = 1.667. Is the work positive, negative or zero?

Answer»

The boundary work is: W = ⌡P dV

P drops but does V go up or down?

The process equation is: PVⁿ = C

so we can solve for P to show it in a P-V diagram

P = CV^-n

as n = 1.667 the curve drops as V goes up we see

V₂ > V₁ giving dV > 0 and the work is then positive.

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Helium gas expands from 125 kPa, 350 K and 0.25 m3 to 100 kPa in a polytropic process with n = 1.667. Is the work positive, negative or zero?

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