Question
Ears pop The middle ear has a volume of about $6.0 \mathrm{cm}^{3}$ when at a pressure of $1.0 \times 10^{5} \mathrm{N} / \mathrm{m}^{2}$. Determine the volume of that same air when the air pressure is $0.83 \times 10^{5} \mathrm{N} / \mathrm{m}^{2},$ as it is at an elevation of $1500 \mathrm{m}$ above sea level (assume the air temperature remains constant). If the volume of the middle ear remains constant, some air will have to leave as theelevation increases. That is why ears "pop."
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Therefore, we can use the ideal gas law in the form of Boyle's law, which states that the product of the pressure and volume of a gas is constant if the temperature is constant. Mathematically, this can be written as: \[P_1V_1 = P_2V_2\] Show more…
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B10 Ears pop The middle ear has a volume of about 6.0 $\mathrm{cm}^{3}$ when at a pressure of $1.0 \times 10^{5} \mathrm{N} / \mathrm{m}^{2}(1.0 \mathrm{atm}) .$ Determine the volume of that same air when the air pressure is $0.83 \times 10^{5} \mathrm{N} / \mathrm{m}^{2}$ , as it is at an elevation of 1500 $\mathrm{m}$ above sea level (assume the air temperature remains constant). If the volume of the middle ear remains constant, some air will have to leave as the elevation increases. That is why ears “pop.”
Ear "popping" is an unpleasant phenomenon sometimes experienced when a change in pressure occurs, for example in a fast-moving elevator or in an airplane. If you are in a two-seater airplane at $3000 \mathrm{m}$ and a descent of $100 \mathrm{m}$ causes your ears to "pop," what is the pressure change that your ears "pop" at, in millimeters of mercury? If the airplane now rises to $8000 \mathrm{m}$ and again begins descending, how far will the airplane descend before your ears "pop" again? Assume a U.S. Standard Atmosphere.
Sometimes when riding an elevator or driving up or down a hilly road a person's ears "pop" as the pressure difference between the inside and outside of the ear is cqualized. Determine the pressure difference (in psi) associated with this phenomenon if it occurs during a 150 -ft elevation change.
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