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
Answers
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
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
Solution :-
Work done = Force × Displacement
But Force = Pressure × Area
So,
Work done = Pressure × Area × Displacement
Work done = Pressure × Volume
(As, Area × Dispalcement is Volume)
Here -
- P = pressure
- V = volume
P = hg
Given that -
- h = height of mercury = 130 mm = 0.13 m
To convert mm into m divide with 1000
- = 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) =
From above P = hg
So,
P =
Substitute the known values in above formula
→ P =
→ P =
→ P =
→ P =
→ P =
•°• Power of the heart is 1.155 W.