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Magazine Problem 58
An emphysema patient is breathing pure \(\mathrm{O}_{2}\) through a face mask.
The cylinder of \(\mathrm{O}_{2}\) contains \(0.60 \mathrm{ft}^{3}\) of
\(\mathrm{O}_{2}\) gas at a pressure of \(2200 \mathrm{lb} / \mathrm{in}^{2} .\)
(a) What volume would the oxygen occupy at atmospheric pressure (and the same
temperature)? (b) If the patient takes in
\(8 \mathrm{L} / \mathrm{min}\) of \(\mathrm{O}_{2}\) at atmospheric pressure, how
long will the cylinder last?
Problem 59
Consider the expansion of an ideal gas at constant pressure. The initial
temperature is \(T_{0}\) and the initial volume is \(V_{0} .\) (a) Show that
\(\Delta V / V_{0}=\beta \Delta T,\) where \(\beta=1 / T_{0}\)
(b) Compare the coefficient of volume expansion \(\beta\) for an ideal gas at
\(20^{\circ} \mathrm{C}\) to the values for liquids and gases listed in Table
13.3
Problem 60
What is the temperature of an ideal gas whose molecules have an average translational kinetic energy of \(3.20 \times 10^{-20} \mathrm{J} ?\)
Problem 61
What is the total translational kinetic energy of the gas molecules of 0.420
mol of air at atmospheric pressure that occupies a volume of $1.00
\mathrm{L}\left(0.00100 \mathrm{m}^{3}\right) ?$
Problem 62
What is the kinetic energy per unit volume in an ideal gas at (a) \(P=1.00\) atm
and (b) \(P=300.0\) atm?
Problem 63
Show that, for an ideal gas,
$$
P=\frac{1}{3} \rho v_{\mathrm{rms}}^{2}
$$
where \(P\) is the pressure, \(\rho\) is the mass density, and \(v_{\mathrm{rms}}\)
is the rms speed of the gas molecules.
Problem 65
What is the total internal kinetic energy of 1.0 mol of an ideal gas at \(0.0^{\circ} \mathrm{C}\) and 1.00 atm?
Problem 66
If 2.0 mol of nitrogen gas \(\left(\mathrm{N}_{2}\right)\) are placed in a cubic
box, \(25 \mathrm{cm}\) on each side, at 1.6 atm of pressure, what is the rms
speed of the nitrogen molecules?
Problem 67
There are two identical containers of gas at the same temperature and pressure, one containing argon and the other neon. What is the ratio of the rms speed of the argon atoms to that of the neon atoms? The atomic mass of argon is twice that of neon. tutorial: RMS speed)
Problem 68
A smoke particle has a mass of \(1.38 \times 10^{-17} \mathrm{kg}\) and it is
randomly moving about in thermal equilibrium with room temperature air at
\(27^{\circ} \mathrm{C} .\) What is the rms speed of the particle?
