= Solution
<Boyle's law> states that a fixed amount of <gas> at constant <temperature> obeys
$$
\boxed{pV=\text{constant},}
$$
where $p$ is absolute <pressure>, not <gauge pressure>. It is an ideal-gas approximation, not an assertion that every rapid compression is isothermal.
The <respiratory diaphragm> contracts and lowers its dome, increasing thoracic volume. Mechanical coupling through the pleural space lets the <lungs> expand; alveolar <pressure> falls below atmospheric <pressure>, drawing air in. Relaxation of the <respiratory diaphragm> and elastic recoil drive quiet expiration. These <respiratory mechanics> describe ventilation, distinct from chemical <cellular respiration>.<How the Lungs Work: What Breathing Does for the Body by the National Heart, Lung, and Blood Institute>[“Breathing in” and “Breathing out”: diaphragm movement, expansion and recoil]{ref}
For the stipulated sealed, isothermal gas, initial and final volumes are $1600$ and $2000\,\mathrm{cm^3}$. Expressing absolute <pressure> as a mercury-column height,
$$
p_f=760\frac{1600}{2000}=608\,\mathrm{mmHg}.
$$
The mercury column is supported by the atmospheric-to-internal <pressure> difference:
$$
\boxed{h=760-608=152\,\mathrm{mm}=15.2\,\mathrm{cm}.}
$$
The specified volume change belongs to the historical idealized model. Real tube-air volume, temperature changes and limits on respiratory-muscle pressure generation would affect a physical apparatus.
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