Question

If the heart pushes 1 cc of blood in one second under pressure 20,000 N m2 , the power of heart is
(A) 0.02 W
(B) 400 W
(C) 5 × 10–10 W
(D) 0.2 W​

Answer 1

Volume of the blood heart pushes (V) = 1 cc

⇒ V = 1 cm³

⇒ V = 10⁻⁶ m³

Time (t) = 1 s

Pressure (P) = 20,000 N/m²

Power : It is defined as work done per unit time

Work done too defined as product of pressure and change in volume

$\pink{\bigstar}\ \; \sf Power=\dfrac{Work}{Time}\\\\\orange{\bigstar}\ \; \sf P=\dfrac{P\Delta V}{t}$

$\to \sf P=\dfrac{20,000\times 10^{-6}}{1}\\\\\to \sf P=2\times 10^5\times 10^{-5}\times 10^{-1}\\\\\to \sf P=2\times 10^{-1}\\\\\to \sf P=0.2\ W$

Power of the heart = 0.2 W

Option D

Answer 2

$\pink{ \underline{ \underline{ \red{ \sf{ Given : }}}}}$

• The pressure of the heart is : 20,000N/m².
• And the change in volume time of the heart is : 1 cc.

or,

➠ V = 1 cm³

➠ V = $\bf{10} ^{-6} m³$

$\pink{ \underline{ \underline{ \red{ \sf{ To \: find : }}}}}$

➠ The power of heart.

$\pink{ \underline{ \underline{ \red{ \sf{ Solution : }}}}}$

We know that,

$\gray \bigstar{ \underline{ \boxed{ \bf{ \red{ power} = \green{\frac{work \: done}{time} }}}}} \gray \bigstar$

Where,

➠ V = $\bf{10} ^{-6} m³$

➠ t = 1 sec

➠ p = 20,000N/m².

$\pink{ \underline{ \underline{ \red{ \sf{ Procedure : }}}}}$

$\longmapsto \sf power = \frac{20000 \times {10}^{ - 6} }{1}$

$\longmapsto \sf power = 2 \times \cancel{10}^{5} \times \cancel{10}^{ - 5} \times {10}^{ - 1}$

$\longmapsto \sf power = 2 \times {10}^{ - 1}$

$\pink \longmapsto \red{\bf power = 0.2W}$

Hence,

Option D is the correct answer i.e., : $\bf\green{<strong> </strong>0.2W }$

$\pink{ \underline{ \underline{ \red{ \sf{ Key \: words : }}}}}$

Work : It can be defined as a product of change in volume and pressure.

Power : Work done/time