The human heart is a powerful and reliable pump. Each day it takes in and discha

Question

The human heart is a powerful and reliable pump. Each day it takes in and discharges about 7500 L of blood. Suppose the work done is equal to that required for lifting this blood a height of 1.292m and that the blood density is that of water, 1.00x10^3 kg/m^3. a) What work in joules is done by the heart in a day? b) What is its power output in watts? c) At a food conversion efficiency of 7.44%, how many food calories ( one food calorie=4190 joules) must be taken from the daily diet for the heart?

Explanation / Answer

Given Volume of the blood, V = 7500 L = 7.5 m3 Height the blood lifted is , h = 1.292 m Density of blood is , = 1.00x10^3 kg/m^3 a) The work done by the heart is , W = mgh where m = *V = (1.00x10^3 kg/m^3) * 7.5 m3             m = 7500 kg Now, W = 7500 kg *9.8 m/s2 *1.292 m               = 9.5 *104 J b) Power out put , P = W / t                                 = ( 9.5 *104 J) / 24 *60*60s                                 = 1.1 W c) The efficiency of the food is 7.44%    since = power output / power input       0.0744 = 1.1 W / Pin        Pin = 14.78 W       Food calories taken per day is , E = Pin *t = 14.78 W * 86400 s                                                      E = 1.27 *106 J 1 Food calorie = 4190 J 1.27 *106 J = 303 food cal     Number of food calories taken is 303

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