Gas from a cylinder of compressed helium is used to inflate an inelastic flexible balloon, originally folded completely flat, to a volume 0.6 m³. If the barometer reads 760 mm Hg, what is the amount of work done upon the atmosphere by the balloon ? Sketch the system before and after the process.

Question

Accepted Answer

Refer Fig. 2.34. The firm line [latex]B_1[/latex] shows the boundary of the system before the process, and dotted line [latex]B_2[/latex] shows the boundary after the process.

The displacement work,

[latex]W_d=\int_{ ext {cylinder }} p d V+\int_{ ext {balloon }} p d V=0+\int_{ ext {balloon }} p d V[/latex]

= 101.325 × 0.6 [[latex]\because[/latex] dV = 0.6 m³]

= 60.795 kJ.

This is a positive work, because the work is done by the system. Work done by the atmosphere is – 60.795 kJ. Since the wall of the cylinder is rigid there is no pdV-work involved in it.

It is assumed that the pressure in the balloon is atmospheric at all times, since the balloon fabric is light, inelastic and unstressed. If the balloon were elastic and stressed during the filling process, the work done by the gas would be greater than 60.795 kJ by an amount equal to the work done in stretching the balloon, although the displacement work done by atmosphere is still – 60.795 kJ. However, if the system includes both the gas and the balloon, the displacement work should be 60.795 kJ, as estimated above.

Question 2.15: Gas from a cylinder of compressed helium is used to inflate ...

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