Ideal gas law

An NBA ball

The air in a regulation NBA basketball has a pressure of 1.54atm and the ball has a radius of 0.119m. Assume the temperature of the air inside the basketball is 25°C (i.e. near room temperature).

a. Determine the number of moles of air inside an NBA basketball.

b. Determine the number of molecules of air inside an NBA basketball.

Ice bath

A gas in a sealed rigid canister starts at room temperature T=293K and atmospheric pressure. The canister is then placed in an ice bath and allowed to cool to a temperature of T=255K.

Determine the pressure of the gas after reaching a temperature of 255K.

First law of thermodynamics

Nitrogen piston

A container has a sample of nitrogen gas and a tightly fitting movable piston that does not allow any of the gas to escape. During a thermodynamics process, 200 joules of heat enter the gas, and the gas does 300 joules of work in the process.

What was the change in internal energy of the gas during the process described above?

Helium

Four identical containers have equal amounts of helium gas that all start at the same initial temperature. Containers of gas also have a tightly fitting movable piston that does not allow any of the gas to escape. Each sample of gas is taken through a different process as described below:

Find the four final temperatures. Which of the following correctly ranks the final temperatures of the samples of gas after they're taken through the processes described above.

A. $T_4>T_3>T_2>T_1$