An entrepreneurial undergraduate student wants to set up a balloon inflation bus
ID: 1861555 • Letter: A
Question
An entrepreneurial undergraduate student wants to set up a balloon inflation business,
and has asked for your help to do some preliminary calculations. You have the following
information:
1. The initial balloon volume is zero.
2. The balloon is inflated to a final pressure of 2.8 bar
3. For V > V0 the pressure inside the balloon, Pi, is given by Pi = Pa + b(V2 V02) where
Pa = 1 bar
b = 1.8 x 108 bar/m6
V is the total volume of the balloon in m3
V0 = 105 m3
Note that the second term on the right hand side of the equation models the
pressure contribution due to the elastic deformation of the balloon.
4. For V < V0 the balloon is limp.
5. The balloon is filled with helium gas, which can be treated as an ideal gas of
constant heat capacity Cv = 1.5 R, where R is the Gas Constant.
6. Helium is available from a compressed gas tank source, and is regulated to 4 bar
and 290 K by a pressure regulator.
7. The balloon is made of a well-insulated rubbery material.
Although you are not impressed with the student?s business plan, you decide to answer
his questions anyway.
(a) How much work is done by the helium gas to inflate the balloon to the volume V0?
(b) What is the balloon temperature when the volume is V0?
(c) How much additional work is done by the helium gas to inflate the balloon beyond
V0 to its final state?
(d) What is the balloon temperature at the end of the inflation process?
Explanation / Answer
work done