Question

Imagine designing an experiment in which the presence of a gas is determined by simply listening to the gas with your ear. The human ear can detect pressures as low as 2 x 10^-5 N*m^-2. Assuming that the eardrum has an area of roughly 1 mm^2, what is the minimum collisional rate that can be detected by ear? Assume that the gas of interest is N2 at 298 K.

Answer 1

Step-by-step explanation:

Pressure = Force/Area

so,

Force =Pressure x Area

Force =(2x 10⁻⁵ )N/M² x (1 x (10⁻³)² M²

Force = 2 x 10⁻¹¹N

as we know,

Force= mass x acceleration ( F=m.a)

a = F/m

a =(2 x 10⁻¹¹N)/28

g since 1 N=1.kg.m.s⁻²

a=(2 x 10-11kg.m.s⁻² )/(28 x 10⁻³kg)

a = 5.6 x 10-7 m.s⁻²

thus minimum collision rate that can be detected is 5.6 x 10-7 m.s⁻²