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Step-by-Step Solution
Step 1: Identify given quantities
• Volume of blood pumped in one minute, $V = 5\,\text{litres} = 5 \times 10^{-3}\,\text{m}^3$
• Time taken, $t = 1\,\text{minute} = 60\,\text{s}$
• Pressure of blood, given as $150\,\text{mm of Hg}$, needs conversion to SI units (N/m2).
Step 2: Convert the pressure from mm of Hg to N/m2
1 mm of Hg corresponds to a height of 0.001 m of mercury column. Thus:
• Height of mercury, $h = 150\,\text{mm} = 0.15\,\text{m}$
• Density of mercury, $\rho = 13.6 \times 10^{3}\,\text{kg}\,\text{m}^{-3}$
• Acceleration due to gravity, $g = 10\,\text{m}\,\text{s}^{-2}$
Using $P = h \, \rho \, g$, we get:
$P = 0.15 \times 13.6 \times 10^{3} \times 10 = 20.4 \times 10^{3}\,\text{N}\,\text{m}^{-2}$
Step 3: Calculate the power of the heart
Power is given by the product of pressure and volume flow rate:
$ \text{Power} = \dfrac{P \times V}{t} $
Substitute the values:
$
\text{Power}
= \dfrac{(20.4 \times 10^{3}) \times (5 \times 10^{-3})}{60}
$
$
= \dfrac{20.4 \times 10^{3} \times 5 \times 10^{-3}}{60}
$
$
= \dfrac{20.4 \times 5 \times 10^{0}}{60}
$
$
= \dfrac{102}{60}
$
$
= 1.70\,\text{W}
$
Final Answer
The power of the man’s heart is $1.70\,\text{W}$.
