21. Kinetic Theory of Ideal Gases

Assuming a typical nitrogen or oxygen molecule is about 0.3 nm in diameter, what percent of the room you are sitting in is taken up by the volume of the molecules themselves?

The semiconductor industry manufactures integrated circuits in large vacuum chambers where the pressure is 1.0×10^-10 mm of Hg. What fraction is this of atmospheric pressure?

A scuba tank when fully charged has an absolute pressure of 185 atm at 18°C. The volume of the tank is 11.3 L. What would the volume of the air be at 1.00 atm and at the same temperature?

A large organic molecule has a mass of $1.41\times {10}^{-21}$ kg. What is the molar mass of this compound?

A gas with initial state variables p₁, V₁, and T₁ expands isothermally until V₂ = 2V₁. What are p₂?

Equation 20.3 is the mean free path of a particle through a gas of identical particles of equal radius. An electron can be thought of as a point particle with zero radius. Electrons travel 3.0 km through the Stanford Linear Accelerator. In order for scattering losses to be negligible, the pressure inside the accelerator tube must be reduced to the point where the mean free path is at least 50 km. What is the maximum possible pressure inside the accelerator tube, assuming T = 20℃? Give your answer in both P_a and atm.

In Problems $67,68,69,$ and $70$ you are given the equation(s) used to solve a problem. For each of these, you are to write a realistic problem for which this is the correct equation(s).

$p_2=\frac{300{\text{ cm}}^3}{100{\text{ cm}}^3}\times 1\times 2\text{ atm}$

0.10 mol of argon gas is admitted to an evacuated 50 cm³ container at 20°C. The gas then undergoes an isochoric heating to a temperature of 300°C. What is the final pressure of the gas?

A cylindrical tank has a tight-fitting piston that allows the volume of the tank to be changed. The tank originally contains $0.110$ m³ of air at a pressure of $0.355$ atm. The piston is slowly pulled out until the volume of the gas is increased to $0.390$ m³. If the temperature remains constant, what is the final value of the pressure?

A 6.0-cm-diameter cylinder of nitrogen gas has a 4.0-cm-thick movable copper piston. The cylinder is oriented vertically, as shown in FIGURE P19.49, and the air above the piston is evacuated. When the gas temperature is 20°C, the piston floats 20 cm above the bottom of the cylinder. What is the new equilibrium temperature of the gas?

The 50 kg circular piston shown in FIGURE P18.57 floats on 0.12 mol of compressed air. What is the piston height h if the temperature is 30°C?

A helium balloon has volume V₀ and temperature T₀ at sea level where the pressure is P₀ and the air density is ρ₀. The balloon is allowed to float up in the air to altitude y where the temperature is T₁. Show that the buoyant force does not depend on altitude y. Assume that the skin of the balloon maintains the helium pressure at a constant factor of 1.05 times greater than the outside pressure. [Hint: Assume that the pressure change with altitude is P = P₀ e⁻ᶜʸ , Eq. 13–6c in Chapter 13.]

On a cool morning, when the temperature is 15°C, you measure the pressure in your car tires to be 30 psi. After driving 20 mi on the freeway, the temperature of your tires is 45°C . What pressure will your tire gauge now show?

A gas with an initial temperature of 900°C undergoes the process shown in FIGURE EX18.35. What type of process is this?

A sauna has 7.8 m³ of air volume, and the temperature is 85°C. The air is perfectly dry. How much water (in kg) should be evaporated if we want to increase the relative humidity from 0% to 10%? (See Table 18–2.)