When a person smokes heavily for some period of time, the walls of their alveoli

Question

When a person smokes heavily for some period of time, the walls of their alveoli start to collapse. Say that this has happened for a particular smoker, producing a lung that has the same total volume but containing alveoli whose average radius has increased 3 fold. If they are to maintain the same energy expenditure rate, how much faster do they now have to breathe? Assume the same volume of air is inhaled in each breath and the flux is constant. Old breathing rate = healthy; New breathing rate = after smoking.

a. New breathing rate = 1 * Old breathing rate
b. New breathing rate = 3 * Old breathing rate
c. New breathing rate = 4 * Old breathing rate
d. New breathing rate = 9 * Old breathing rate
e. New breathing rate = 27 * Old breathing rate.

Explanation / Answer

         concept:          Since,           For a particular smoker, producing a lung that has the same total volume but containing alveoli whose average radius has increased = R'= 3 fold and   maintain the same energy expenditure rate, same volume of air is inhaled in each breath and the flux is constant   ,         Here ,the change of radious results ,alveoli   volume has to be                   increased to R3 times ( the shape of alveoli assumed to be hallow sphere)                     However ,lung has the same total volume                  thus, for 3 - fold incerased of radious will gives                             (3)3 = 27 increase of alveoli   volume                 Thus, this change in volume of alveoli   brings the        If the    Old breathing rate = healthy    and                    New breathing rate = after smoking                      give us to : New breathing rate = 27 * Old breathing rate
                          Since,           For a particular smoker, producing a lung that has the same total volume but containing alveoli whose average radius has increased = R'= 3 fold and   maintain the same energy expenditure rate, same volume of air is inhaled in each breath and the flux is constant   ,         Here ,the change of radious results ,alveoli   volume has to be                   increased to R3 times ( the shape of alveoli assumed to be hallow sphere)                     However ,lung has the same total volume                  thus, for 3 - fold incerased of radious will gives                             (3)3 = 27 increase of alveoli   volume                 Thus, this change in volume of alveoli   brings the        If the    Old breathing rate = healthy    and                    New breathing rate = after smoking                      give us to : New breathing rate = 27 * Old breathing rate
                

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