A player throws a basketball (horizontally) against a wall, compressing the ball

Question

A player throws a basketball (horizontally) against a wall, compressing the ball to 80% of its original volume. The initial diameter of the ball is 23.9 cm. The ball is filled with Nitrogen gas (which behaves like an ideal gas) and is initially at a temperature of 20.2 celsius and pressure of 2 atm. At the point of maximum compression, the pressure inside the ball rises to 2.73 atm. What is the work done by the player on the ball? (Assume that the compression of the ball is adiabatic and that there are no other losses in energy)

Explanation / Answer

For nitrogen gas,

gamma = 7/5 = 1.4

Work done = nR deltaT / (1-gamma)

    = delta (pV) /(1-gamma)

   = 101300*(4/3)*pi*(0.1195^3)*[ -2 + 2.73*0.8]/0.4

= 333 J

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