Question

A human heart pumps $70{\text{ }}CC$ of blood at each beat against a pressure of $72{\text{ }}mm$ of Hg. If the pulse frequency is $72$ per minute the power of the heart is
A. $1.2{\text{ }}W$
B. $1.4{\text{ }}W$
C. $1.6{\text{ }}W$
D. $0.8{\text{ }}W$

Answer 1

Hint:We know that we have to find out Power so we use the formula of power as power is defined as the time required to complete a work done. There are various formulas to find Work Done but in this particular case as the pressure and change of volume given so we will make use of them to find work and then divide with time to get the result. Density of mercury is $13.6{\text{ }}g.c{m^{ - 3}}$.

Complete step by step answer:
We will use Work done $(W) = PdV$. The above question is assigned with different values so we have to make use of them to find the respective solution. Firstly, we have to find out the pressure$(P)$ from the above values,
We know that,
$P = h\rho g$
Where height $(h)$$ = $$72{\text{ }}mm$ of Hg$ = 72 \times {10^{ - 3}}{\text{ }}m$ of Hg.
Density$(\rho )$$ = 13600{\text{ }}kg.{m^{ - 3}}$
Acceleration due to gravity $(g) = 9.8{\text{ }}m.{s^{ - 2}}$
$P = 72 \times {10^{ - 3}} \times 13600 \times 9.8 \\
\Rightarrow P = 9596.16{\text{ }}Pascal - - - - - - (1) \\ $
Now, as the frequency of heart beat is given then we must have to find out the total change in volume.In one beat the total amount of change in volume $dV$ is $70{\text{ }}CC$$ = 70 \times {10^{ - 6}}{\text{ }}{m^3}$
Let $d{V_T}$ be the total change in volume.
Then $d{V_T}$$ = 70 \times {10^{ - 6}} \times 72$
$ \Rightarrow d{V_T} = 5040 \times {10^{ - 6}}\,{m^3} - - - - - - (2)$
Now we have to convert time in seconds so, $t = 60{\text{ }}s - - - - - - (3)$

Therefore by putting the values of $\left( 1 \right),\left( 2 \right),\left( 3 \right)$ in the formula Power$ = \dfrac{{Pd{V_T}}}{t}$ we get,
$\text{Power}= \dfrac{{9596.16 \times 5040 \times {{10}^{ - 6}}}}{{60}} \\
\therefore \text{Power}= 0.80{\text{ }}Watt $
Hence, the power generated when human heart pumps $70{\text{ }}CC$ of blood at each beat against a pressure of $72{\text{ }}mm$ of Hg with pulse frequency $72$ per minute is $0.80{\text{ }}Watt$.

Hence, the correct answer is option D.

Note:We must change the change $dV$(change in volume in per minute) to $d{V_T}$ (total change in volume in per minute). Where, $d{V_T}$$ = n \times dV$ where n is the number of frequencies. We must consider time in seconds every time.