Question

After exhalation, human alveoli have an average radius of approximately 0.05 mm. When inflated by inhalation, the radius increases to about 0.10 mm. The normal mucous tissue fluid surrounding the alveoli has a nominal surface tension of about 50 dynes/cm. The presence of the natural surfactant decreases this to about 3.3 dynes/cm (a factor of 15!). Note that the lungs are inflating by applying a negative pressure to body cavity around them, so the signs of your pressure changes might look a little odd at first.

1. The units “dynes/cm” do not look right for surface energy at first glance because of the linear cm units. Convert the two given surface tensions (with and without surfactant) to units of J/m2 to show why dynes/cm units make sense.

2. Using the converted J/m2 units, calculate the applied pressure necessary to inflate the alveoli without the surfactant, in units of Torr.

3. Calculate the applied pressure necessary to inflate the alveoli with the surfactant, in units of Torr.

4. By what factor has the addition of the surfactant changed the inhalation pressure?

Answer 1

GIVEN: - Radine of alveoli= 0.05 mm • bu & - 0.10nm (deflated) infla Surface tension of the normal mucous tissue luid around alveol = 50 dynes/cm In the presence of surfactant - 3.3 dy mesſen) SOLUTION :- Surface tension is basically attraction of the I articles in the surface layer by the bulk of the liquid which tende to minimize the surface area. surface Tension is the reason why drops are round. Surface Tension (s) is force fee unit length and has wit Newton/m S= Force orce = N (SI unit) length in surface IN has los dyne Im has loon drop force suficiente de op घाट

we will fast convent see how many Dyne/ con are in I Newton/m - Layne : 10-5 N 10-2 m Dyne / em? 103 N/m] Iem So to convert the given valuce inte si 1 units we need to multiply them by value of 's (surface tension) Without surfactant - 50x163 N/m with surfactant - 3.3 X 10 3 N/m 1036 Now Joule/m² is a unit of force. We can check that by simply wing to following strategy Newton & Force = mass x acceleration metre length tt length = [MILKT 2 2 [MT-2] L] Joule & Energy & Forcexlength a [MT-2] (metre)” beryth) where, [M7 is mass IT is time [L7 is length.

Since out a 1 1 Joule 1 Nm nol s1 unit) So ou 1 Soule/m² - 1 N/m Hence, Soule/me is just anothee way of writing N/ m s NOCO Sulface tension without With 12 surfactant 50x10s ? Joulem 3.3x10 3 Joule /m² Now, The pressure needed to inflate the alveole without the surfactant would be de 0.10 mm - 0.10 x 10-3 m radius of inflated alecol) Pressure can be found by formule Pressures P-45 surface tension e radius of the bubble here the alveoli will behaul as a bubble Putting the values

P2 Joule/m² 4X 500 10 3 0.10X10-3 m 2000 Pascal Pe *1 Pascal = 0.0075 torr 2000 Paz 0.00758 2000 2 15 tore Pressure needed to infeate the alveoli with the surfactant 1 S = 3.3x10-3 Youle/m² P2 45, 4X 3.3x103 N/m2 al Pa 0.10X 10-3 2 732 A - 0.099 hore We can clearly see that in the presence of surfactant 10.099 fore i.e. 450 times smalece than the pressure needed for in the absence of sulfaclaut.