Chapter 1: Q89P (page 200)

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 $1.05 \times 10^{3} k g / m^{3}$ . (a) How much work does the heart do in a day? (b) What is the heart’s power output in watts?

Short Answer

Expert verified

a) The required work done is $1.26 \times 10^{5} J$ .

b) The heart’s power output is $1.46 W$ .

Step by step solution

Identify the given data

The volume of the blood is $V = 7500 L (\frac{10^{- 3} m^{3}}{1 L}) = 7.500 m^{3}$ .

The density of the blood is $ρ = 1.05 \times 10^{3} k g / m^{3}$ .

Height of distance is $S = 1.63 m$ .

The time during the day is $t = 1 d a y (\frac{86400 s}{1 d a y}) = 86400 s$ .

Concept/Significance of Work done

The expression of work done is given by,

W = FS

W = mgS

W = pVgs…………………..(1)

Determine the work done by heart in one day(a)

Substitute all the values in equation (1), and we get,

$W = (1.05 \times 10^{3} k g / m^{3}) (7.500 m^{3}) (9.8 m / s^{2}) (1.63) = 1.26 \times 10^{5} J$

Therefore, the required work done is $1.26 \times 10^{5} J$ .

Determine the heart’s power output in watts(b)

The expression for power is given by,

$P = \frac{W}{t}$ ………………….(2)

Substitute all the values in equation (2), and we get,

$P = \frac{1.26 \times 10^{5} J}{86400} = 1.46 W$

Therefore, the heart’s power output is 1.46 W .

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Short Answer

Step by step solution

Identify the given data

Concept/Significance of Work done

Determine the work done by heart in one day(a)

Determine the heart’s power output in watts(b)

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