A player bounces a basketball on the floor, compressing it to 80.0% of its original volume. The air (assume it is essentially N2 gas) inside the ball is originally at 20.0o C and 2.00 atm. The ball’s inside diameter is 23.9 cm. (a) What temperature does the air in the ball reach at its maximum compression? Assume the compression is adiabatic and treat the gas as ideal. (b) By how much does the internal energy of the air change between the ball’s original state and its maximum compression?

Solution to 34E Step 1 Initial pressure=2 atm Initial temperature =20 C=293.15K -2 Diameter of ball=23.9cm =23.9x10 m Radius of the ball=11.95x10 m -2 3 -33 Initial Volume =(4/3)r =7.15x10 m -3 3 -33 Final volume =0.8x7.15x10 m =5.7x10 m Molar mass of nitrogen=28.13g/mol R=8.314 Step 2 Since it is an adiabatic compression, V T = T ( 1 )1 …………………………………………….. = 1.4 for diatomic gas 2 1 V2 1 0.4 T 2 293.15( 0.8) T=320.3K