2. An elastic balloon filled with gas has a diameter of 0.3 m and an internal pr

Question

2. An elastic balloon filled with gas has a diameter of 0.3 m and an internal pressure of 150kPa. The gas is heated until the balloon has a diameter of 0.4m and an internal pressure of 200 kPa. Assume that the heating process takes place quasi-statically, and that the internal pressure in the balloon is proportional to the balloon's diameter. (a) Calculate the work done by the gas on the balloon during the heating process. (b) Calculate the work done by the balloon on the atmosphere. Assume the atmospheric pressure is a constant 101.3 25 kPa.

Explanation / Answer

(a) As work done is given by

W = d(PV) = P2V2 - P1V1

Using initial and final values of pressure and volume:

Work done by gas is given by:

4/3 x 3.141592 x ( 0.23 x 2 x 105 - 0.153x 1.5 x 105)

Or

W = 4.58 kJ

This is work done by gas in infalting the balloon.

(b) Now the pressure of atmosphere remains constant at 101325 Pa

Hence, work done is given by

W = d(PV) = P dV

As P is constant

Hence,

W = P x change in volume due to inflation of balloon

W = 4/3 x 3.141592 x 101325 (0.153 - 0.23)

W = -1.962 kJ

Is required work done by atmosphere

Work done on atmosphere is 1.962 kJ

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