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Magazine Problem 48
A constant volume gas thermometer containing helium is immersed in boiling
ammonia \(\left(-33^{\circ} \mathrm{C}\right)\) and the pressure is read once
equilibrium is reached. The thermometer is then moved to a bath of boiling
water \(\left(100.0^{\circ} \mathrm{C}\right) .\) After the manometer was
adjusted to keep the volume of helium constant, by what factor was the
pressure multiplied?
Problem 49
A hydrogen balloon at Earth's surface has a volume of \(5.0 \mathrm{m}^{3}\) on
a day when the temperature is \(27^{\circ} \mathrm{C}\) and the pressure is
\(1.00 \times 10^{5} \mathrm{N} / \mathrm{m}^{2} .\) The balloon rises and
expands as the pressure drops. What would the volume of the same number of
moles of hydrogen be at an altitude of \(40 \mathrm{km}\) where the pressure is
\(0.33 \times 10^{3} \mathrm{N} / \mathrm{m}^{2}\) and the temperature is
\(-13^{\circ} \mathrm{C} ?\)
Problem 50
An ideal gas that occupies \(1.2 \mathrm{m}^{3}\) at a pressure of $1.0 \times
10^{5} \mathrm{Pa}\( and a temperature of \)27^{\circ} \mathrm{C}$ is compressed
to a volume of \(0.60 \mathrm{m}^{3}\) and heated to a temperature of
\(227^{\circ} \mathrm{C} .\) What is the new pressure?
Problem 51
A diver rises quickly to the surface from a 5.0 -m depth. If she did not
exhale the gas from her lungs before rising, by what factor would her lungs
expand? Assume the temperature to be constant and the pressure in the lungs to
match the pressure outside the diver's body. The density of seawater is $1.03
\times 10^{3} \mathrm{kg} / \mathrm{m}^{3}$
Problem 52
In intergalactic space, there is an average of about one hydrogen atom per
\(\mathrm{cm}^{3}\) and the temperature is \(3 \mathrm{K}\) What is the absolute
pressure?
Problem 53
A tank of compressed air of volume \(1.0 \mathrm{m}^{3}\) is pressurized to 20.0
atm at \(T=273 \mathrm{K}\). A valve is opened and air is released until the
pressure in the tank is 15.0 atm. How many air molecules were released?
Problem 54
A mass of \(0.532 \mathrm{kg}\) of molecular oxygen is contained in a cylinder
at a pressure of \(1.0 \times 10^{5} \mathrm{Pa}\) and a temperature of
\(0.0^{\circ} \mathrm{C} .\) What volume does the gas occupy?
Problem 55
A bubble rises from the bottom of a lake of depth \(80.0 \mathrm{m},\) where the temperature is \(4^{\circ} \mathrm{C} .\) The water temperature at the surface is \(18^{\circ} \mathrm{C} .\) If the bubble's initial diameter is \(1.00 \mathrm{mm},\) what is its diameter when it reaches the surface? (Ignore the surface tension of water. Assume the bubble warms as it rises to the same temperature as the water and retains a spherical shape. Assume \(\left.P_{\mathrm{atm}}=1.0 \mathrm{atm} .\right)\)
Problem 56
A bubble with a volume of \(1.00 \mathrm{cm}^{3}\) forms at the bottom of a lake
that is \(20.0 \mathrm{m}\) deep. The temperature at the bottom of the lake is
\(10.0^{\circ} \mathrm{C} .\) The bubble rises to the surface where the water
temperature is \(25.0^{\circ} \mathrm{C}\) Assume that the bubble is small
enough that its temperature always matches that of its surroundings. What is
the volume of the bubble just before it breaks the surface of the water?
Ignore surface tension.
Problem 57
A scuba diver has an air tank with a volume of \(0.010 \mathrm{m}^{3}\) The air
in the tank is initially at a pressure of \(1.0 \times 10^{7} \mathrm{Pa}\)
Assuming that the diver breathes \(0.500 \mathrm{L} / \mathrm{s}\) of air, find
how long the tank will last at depths of (a) \(2.0 \mathrm{m}\) and (b) $20.0
\mathrm{m} .\( (Make the same assumptions as in Example \)13.6 .)$
