21. Kinetic Theory of Ideal Gases

Show that the bulk modulus (Section 12–5) for an ideal gas held at constant temperature is B = P, where P is the pressure.

A 6.0-cm-diameter, 10-cm-long cylinder contains 100 mg of oxygen (O₂) at a pressure less than 1 atm. The cap on one end of the cylinder is held in place only by the pressure of the air. One day when the atmospheric pressure is 100 kPa, it takes a 184 N force to pull the cap off. What is the temperature of the gas?

A cylinder contains nitrogen gas. A piston compresses the gas to half its initial volume. Afterward, has the mass density of the gas changed? If so, by what factor? If not, why not?

0.0050 mol of gas undergoes the process 1→2→3 shown in FIGURE EX18.37. What are temperature T₁?

A gas at 100°C fills volume V₀. If the pressure is held constant, what is the volume if the Kelvin temperature is doubled?

3 moles of an ideal gas fill a cubical box with a side length of 30cm. If the temperature of the gas is 20°C, what is the pressure inside the container?

Hydrogen gas behaves very much like an ideal gas. If you have a sample of Hydrogen gas with a volume of 1000 cm³ at 30°C with a pressure of 1 × 10⁵ Pa, calculate how many hydrogen atoms (particles) there are in the sample.

A balloon contains 3900cm³ of a gas at a pressure of 101 kPa and a temperature of –9°C. If the balloon is warmed such that the temperature rises to 28°C, what volume will the gas occupy? Assume the pressure remains constant.

A constant-volume gas thermometer registers an absolute pressure corresponding to $325$ mm of mercury when in contact with water at the triple point. What pressure does it read when in contact with water at the normal boiling point?

The pressure of a gas at the triple point of water is $1.35$ atm. If its volume remains unchanged, what will its pressure be at the temperature at which CO₂ solidifies?

A large cylindrical tank contains $0.750$ m³ of nitrogen gas at $27$°C and $7.50\times {10}^3$ Pa (absolute pressure). The tank has a tight-fitting piston that allows the volume to be changed. What will be the pressure if the volume is decreased to $0.410$ m³ and the temperature is increased to $157$°C?

You have several identical balloons. You experimentally determine that a balloon will break if its volume exceeds $0.900$ L. The pressure of the gas inside the balloon equals air pressure ($1.00$ atm). If the air inside the balloon is at a constant $22.0$°C and behaves as an ideal gas, what mass of air can you blow into one of the balloons before it bursts?