BIO Power of the Human Heart.? The human heart is a powerful and extremely reliable pump. Each day it takes in and discharges about 7500 L of blood. Assume that the work done by the heart is equal to the work required to lift this amount of blood a height equal to that of the average American woman (1.63 m). The density (mass per unit volume) of blood is 1.05 X 103 kg/m3. (a) How much work does the heart do in a day? (b) What is the heart’s power output in watts?

Solution 95P Step 1: Amount of blood pumped by the heart in a day, V = 7500 L 3 We know that, 1 m = 1000 L Therefore, 1 L = 1/1000 m 3 Therefore, V = 7500 × 1/1000 m = 7.5 m 3 3 3 3 Density of the human blood, d = 1.05 × 10 kg/m Equation for calculating the density, d = ,m/V Where, m - mass of blood V - volume of blood’ Therefore, m = Vd 3 3 3 3 m = 7.5 m × 1.05 × 10 kg/m = 7.875 × 10 kg The amount of blood passing through the heart in a day, m = 7.875 × 10 kg 3 Step 2: a) Work done by the heart, W = FS Where, F = Force to pump the blood up to a height S = Distance of pumping the blood. F = mg Where, g - acceleration due to gravity Therefore, here, we can write, W = mgh h = 1.63 m (Provided) W = 7.875 × 10 kg × 9.8 m/s × 1.63 m = 125.8 × 10 J 3 The work done by the heart to pump blood daily will be, W = 125.8 × 10 J 3