BackA 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?
14 g of nitrogen gas at STP are pressurized in an isochoric process to a pressure of 20 atm. What are the final temperature?
A 1.0 m ✕ 1.0 m ✕ 1.0 m cube of nitrogen gas is at 20℃ and 1.0 atm. Estimate the number of molecules in the cube with a speed between 700 m/s and 1000 m/s.
Photons of light scatter off molecules, and the distance you can see through a gas is proportional to the mean free path of photons through the gas. Photons are not gas molecules, so the mean free path of a photon is not given by Equation 20.3, but its dependence on the number density of the gas and on the molecular radius is the same. Suppose you are in a smoggy city and can barely see buildings 500 m away. How far would you be able to see if the temperature suddenly rose from 20°C to a blazing hot 1500°C with the pressure unchanged?
Interstellar space, far from any stars, is filled with a very low density of hydrogen atoms (H, not H₂). The number density is about 1 atom/cm³ and the temperature is about 3 K. Estimate the pressure in interstellar space. Give your answer in Pa and in atm.
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 Pa and atm.
What is the pressure inside a 41.0-L container holding 105.0 kg of argon gas at 21.6°C?
A standard cylinder of oxygen used in a hospital has gauge pressure = 2000 psi (13,800 kPa) and volume = 14L (0.014m3) at T = 295 K . How long will the cylinder last if the flow rate, measured at atmospheric pressure, is constant at 2.0 L/min?
If a scuba diver fills his lungs to full capacity of 4.8 L when 9.0 m below the surface of sea water, to what volume would his lungs expand if he quickly rose to the surface? Is this advisable?
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?
How well does the ideal gas law describe the pressurized air in a scuba tank? To fill a typical scuba tank, an air compressor intakes about 2300 L of air at 1.0 atm and compresses this gas into the tank’s 12-L internal volume. If the filling process occurs at 20°C, show that a tank holds about 96 mol of air.
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?
What is the partial pressure of water on a day when the temperature is 25°C and the relative humidity is 75%?
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 volume occupied by the balloon is then where .
Using the ideal gas law, find an expression for the mean free path ℓM that involves pressure and temperature instead of (N/V). Use this expression to find the mean free path for nitrogen molecules at a pressure of 7.5 atm and 300 K.