Answer to Question #228334 in Molecular Physics | Thermodynamics for usc

Question

How deep would you have to dive before the air in your middle ear would be

compressed to 75% of its initial volume? Assume for the beginning that the

temperature of the sea is constant as you dive. Take the atmospheric pressure at

height h = 0 is 0.1MPa, ρ is the density of water at 20 degrees Celsius 998.23 kg/ 𝑚3,

g = 9.81 𝑚𝑠-2

Answer 1

$P_iv_i=P_fv_f$

$P_iv_i=(P_i+\rho gh)v_f$

$\rho g h=\frac{P_iv_i}{v_f}-P_i$

$h=\frac{\frac{P_iv_i}{v_f}-P_i}{\rho g}$

Where

$\rho=998.23kg/m^3\\p=0.1Mpa\\v_f=\frac{3}{4}v_i$

Put value

$h=\frac{\frac{P_iv_i}{\frac{3}{4}v_i}-P_i}{\rho g}$

$h=\frac{\frac{4P_i}{3}-P_i}{\rho g}$

$h=\frac{\frac{P_i}{3}}{\rho g}$

$h=\frac{\frac{0.1\times10^6}{3}}{998.23\times 9.81}=3.40m$