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A balloon which is initially collapsed and flat is slowly filled with a gas at 100 kPa so as to form it into a sphere of 1m radius. What is the work done by the gas in the balloon during the filling process?

A balloon which is initially collapsed and flat is slowly filled with a gas at 100 kPa so as to form it into a sphere of 1m radius. What is the work done by the gas in the balloon during the filling process? Correct Answer 418.9 kJ

Concept:

The work done by the gas in the balloon is given by 

W = ∫ pint dv

Here gas is being filled at a constant pressure of 100 kPa,

W = p ∫ dv = p (v2 - v1)

Calculation:

From given, v1 = 0, p = 100 kPa,

v2 = 4/3 (π r3) = 4π/3 = 4.1888 m3

Work done = 100 (4.1888 - 0) = 418.88 = 418.9 kJ 

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