Question

In each heartbeat, a heart pumps 80 ml of blood at an average pressure of 100 mm of Hg. Assuming 60 heart beats per second, the power output of heart is
$({{\rho }_{Hg}}=13.6\times {{10}^{3}}kg{{m}^{-3}})(g=9.8m{{s}^{-3}})$

\text{A}\text{. }60.97W \\\ \text{B}\text{. }63.97W \\\ \text{C}\text{. }1.12W \\\ \text{D}\text{. }83.97W \\\ \end{array}$$

Answer 1

We all know that beating of the heart is nothing pumping blood too. On a single beat, blood from the heart gets pumps. That blood exerts a pressure known as blood pressure which we generally measured in 100mm of Hg. We also know that , Work done is nothing but pressure applied over a volume while power is equal to the work done per unit time. Here to calculate the power of the heat, we can first calculate work done by the heart and then the power.

Complete step-by-step solution
Generally, within 1 minute, if our heart beats for 72 times then we consider our heart is healthy and blood flow is also regular.
In the given question, it is given that, in each heartbeat, the heart pumps volume of 80ml of blood at an average pressure of 100 mm of Hg.
Since $1ml={{10}^{-6}}{{m}^{3}}$, The volume given in ml can be converted into ${{m}^{3}}$ by multiplying it by a factor of ${{10}^{-6}}$
Thus, we have $80ml=80\times {{10}^{-6}}{{m}^{3}}$
In this question, we have to find the power output of the heart. We know that work done is nothing but pressure times volume.
Mathematically.$W=pdv$
Where, $dV=heart\; beat\times volume\; pumped= 60\times (80\times {{10}^{-6}})=4800\times {{10}^{-6}}{{m}^{3}}$
We have pressure given by 100 mm of Hg. To convert it into pascal, we get
$P=\dfrac{100}{760}\times {{10}^{5}}\times 101Pa=1.33\times {{10}^{4}}Pa$
Now rearranging and substituting in the work done equation, we get,
$\text{Power = }\dfrac{\text{work done}}{\text{time}}$
Power $=\dfrac{1.33\times {{10}^{4}}\times 60\times 80\times {{10}^{-5}}}{60\sec }=1.06W$
Hence, the power output of heart is $1.06\;W$ . Therefore option (C) is the correct option.

Note: The term energy and power are closely related to each other but they are not the same by physical quantity. In simple words, energy is known as the ability to cause change while power is known as the rate energy is moved, or used. Work done is generally referred in relation to the force applied with distance while energy is mainly used in reference to other factors