Question

The human heart pumps the average adult’s $6.0L(6000c{m}^3)$of blood through the body every minute. The heart must do work to overcome frictional forces that resist blood flow. The average adult blood pressure is $1.3\times {10}^{4}N/m^2.$

a. How much work does the heart do to move the $6.0L$of blood completely through the body?

b. What power output must the heart have to do this task once a minute?

Hint: When the heart contracts, it applies force to the blood. Pressure is $force/area.$Model the circulatory system as a single closed tube, with cross-section area $A$and volume$V=6.0L,$ filled with blood to which the heart applies a force.

Short answer

a. Work done by the heart is $78J$

b. The output power of the heart is$1.3Watts$

Step-by-step solution

Given information

The human heart pumps the average adult’s $V=6.0L=6\times {10}^{-3}{m}^3$of blood

The average adult blood pressure is $P=1.3\times {10}^{4}N/m^2.$

Time taken$t=1min=60s$

Explanation (Part a) 

The heart do to move the $V$of blood completely through the body.

Work done is given by

$W=PV=1.3\times {10}^4\times 6\times {10}^{-3}=78J$

The work done by the heart is$78J$

Explanation (part b)

The power of the heart is given by

$Power=\frac{W}{t}=\frac{78}{60}=1.3Watts$

The output power of the heart is$1.3Watts$