Chapter 10, Problem 79GP

To determine

To Find: The power output of the heart.

Answer to Problem 79GP

The power output of the heart is $1.14\text{ watt}$ .

Explanation of Solution

Given info:

Volume, $V=70{\text{ cm}}^{\text{3}}\text{=}70\times {10}^{-6}{\text{ m}}^{\text{3}}$

Pressure, $P=105\text{ mm - Hg}$

  $1\text{ mm - Hg = }133\text{ Pa}$

Time,

  $\begin{array}{l}t=1/p=1/\left(70\text{ beats / minute }\right)\\ t=60/70\text{ s}\end{array}$

Formula used:

Write the expression for work.

  $\text{Work }W\text{ = Force }(F)\times \text{Distance }(\Delta l)$

Write the expression for pressure .

  $\text{Pressure }\mathrm{P}\text{ = }\frac{\text{Force }(F)}{\text{Area }(A)}$

Write the expression for force.

  $\text{Force }(F)=P\times A$

Write the expression for power.

  $\begin{array}{l}p=\frac{\text{Work}}{\text{Time}}\\ p=\frac{P\times A\times \Delta l}{t}\\ p=\frac{P\times V}{t}\end{array}$

Calculation:

Substitute the given values in the above equation,

  $\begin{array}{l}p=\frac{P\times V}{t}\\ p=\frac{105\text{ mm - Hg}\times 133\text{ Pa / }1\text{ mm - Hg}\times 70\times {10}^{-6}}{\frac{60}{70}\text{ s}}\\ p=1.14\text{ watt}\end{array}$

Conclusion:

Thus, the power output of the heart is $1.14\text{ watt}$ .