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Magazine Problem 69
Find the rms speed in air at \(0.0^{\circ} \mathrm{C}\) and 1.00 atm of
(a) the \(\mathrm{N}_{2}\) molecules, (b) the \(\mathrm{O}_{2}\) molecules, and
(c) the \(\mathrm{CO}_{2}\) molecules.
Problem 70
What are the rms speeds of helium atoms, and nitrogen, hydrogen, and oxygen
molecules at \(25^{\circ} \mathrm{C} ?\)
Problem 71
If the upper atmosphere of Jupiter has a temperature of
\(160 \mathrm{K}\) and the escape speed is \(60 \mathrm{km} / \mathrm{s}\), would
an astronaut expect to find much hydrogen there?
Problem 72
a sealed cylinder contains a sample of ideal gas at a pressure of 2.0 atm. The
rms speed of the molecules is \(v_{0} .\) If the rms speed is then reduced to
\(0.90 v_{0},\) what is the pressure of the gas?
Problem 73
What is the temperature of an ideal gas whose molecules in random motion have an average translational kinetic energy of \(4.60 \times 10^{-20} \mathrm{J} ?\)
Problem 74
Show that the rms speed of a molecule in an ideal gas at absolute temperature
\(T\) is given by
$$v_{\mathrm{rms}}=\sqrt{\frac{3 k T}{m}}$$
where \(k\) is Boltzmann's constant and \(m\) is the mass of a molecule.
Problem 75
Show that the rms speed of a molecule in an ideal gas at absolute temperature \(T\) is given by $$v_{\mathrm{rms}}=\sqrt{\frac{3 R T}{M}}$$ where \(M\) is the molar mass-the mass of the gas per mole.
Problem 78
At high altitudes, water boils at a temperature lower than $100.0^{\circ}
\mathrm{C}$ due to the lower air pressure. A rule of thumb states that the
time to hard-boil an egg doubles for every \(10.0^{\circ} \mathrm{C}\) drop in
temperature. What activation energy does this rule imply for the chemical
reactions that occur when the egg is cooked?
Problem 79
Estimate the mean free path of a \(\mathrm{N}_{2}\) molecule in air at (a) sea
level \((P \approx 100 \mathrm{kPa} \text { and } T \approx 290 \mathrm{K}),\)
(b) the top of \(\quad\) Mt. Everest (altitude $=8.8 \mathrm{km}, P \approx 50
\mathrm{kPa},\( and \)T \approx 230 \mathrm{K}),\( and \)(\mathrm{c})$ an altitude
of \(30 \mathrm{km}(P \approx 1 \mathrm{kPa}\) and
\(T=230 \mathrm{K}) .\) For simplicity, assume that air is pure nitrogen gas.
The diameter of a \(\mathrm{N}_{2}\) molecule is approximately \(0.3 \mathrm{nm}\)
Problem 80
About how long will it take a perfume molecule to diffuse a distance of $5.00
\mathrm{m}\( in one direction in a room if the diffusion constant is \)1.00
\times 10^{-5} \mathrm{m}^{2} / \mathrm{s} ?$ Assume that the air is perfectly
still-there are no air currents.
