Question

2. The heart of a woman pumps 4 litre of blood per minute at a pressure of
130 mm of mercury. If the density of mercury is 13.6 g cm2 , Calculate the
power of the heart.
(a) 1.144 W
(b) 2.145 W
(C) 1.155 W
(d) 3.155 W​

Answer 1

Answer:

1.155 W

Explanation:

V = volume = 4 L  

h = pressure = 130 mm of mercury  

p = density = 13.6 gm/cm^3  

t = time = 1 minute  

The Volume of blood  

V = 4 litres  

V = 4 x 10^3 cm^3  

V = 4 x 10^-3 m^3  

Work done is given by the formula --> Force x Distance  

Note that Force = Pressure x Area, & Volume = Area x Distance  

Therefore:  

Work = Force x Distance  

Work = Pressure x Area x Distance  

Work = Pressure x Volume  

Work = (h)(p)(g)(V)  

Power is Work "over" time = hpgV / t  

We already know:  

v = volume = 4 L => 4x10^-3 m^3  

h = pressure = 130 mm of mercury => 0.13 m  

p = density = 13.6 gm/cm^3 = 13.6x10^3  

t = 1 minute => 60 seconds  

The extra variable is:  

g = gravity = 9.8 m/s^2  

Plug these numbers into the Power equation:  

Power = hpgV/t  

Power = [(0.13)(13.6x10^3)(9.8)(4x10^-3)]/(60)  

Power = 69.3056 / 60  

Power = 1.155093  

Answer 2

Correct Question

The heart of a woman pumps 4 litres of blood per minute at a pressure of 130 mm of mercury. If the density of mercury is 13.6 g/cm³. Calculate the power of the heart.

Answer

Option (c) 1.155 W

$\rule{100}2$

Solution :-

Work done = Force × Displacement

But Force = Pressure × Area

So,

Work done = Pressure × Area × Displacement

$\therefore$ Work done = Pressure × Volume

(As, Area × Dispalcement is Volume)

Here -

• P = pressure
• V = volume

P = h$\sf{\rho}$g

Given that -

• h = height of mercury = 130 mm = 0.13 m

To convert mm into m divide with 1000

• $\sf{\rho}$ = density of mercury = 13.6 g/cm³
• V = volume = 4 litres = 0.004 m³
• t = time = 60 sec

As, the heart pumps blood per minute.

To convert litres into m divide with 1000

Now,

Power (P) = $\sf{\dfrac{Work\:done}{time}}$

From above P = h$\sf{\rho}$g

So,

P = $\sf{\dfrac{h{\rho}g\:\times\:V}{t}}$

Substitute the known values in above formula

→ P = $\sf{\dfrac{0.13\:\times\:13.6\:\times\:1000\:\times\:9.8\:\times\:0.004}{60}}$

→ P = $\sf{\dfrac{1768\:\times\:9.8\:\times\:0.004}{60}}$

→ P = $\sf{\dfrac{17326\:\times\:0.004}{60}}$

→ P = $\sf{\dfrac{69.3056}{60}}$

→ P = $\sf{1.155}$

•°• Power of the heart is 1.155 W.