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The heart of a man pump s 5 litres of blood through the arteries per minute at a pressure of 150 mm of mercury. If the density of mercury be 13. × 103kg/m3 and g=10m/s2 then the power of heart in watt is
- a)3.0
- b)1.50
- c)1.70
- d)2.35
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
The heart of a man pump s 5 litres of blood through the arteries per ...
To calculate the power of the heart, we need to first determine the work done by the heart and then divide it by the time taken.
Work Done by the Heart:
Work done by the heart can be calculated using the formula:
Work = Force x Distance
In this case, the force is the pressure exerted by the heart and the distance is the volume of blood pumped per minute.
Force:
The pressure exerted by the heart is given as 150 mm of mercury. To convert this to SI units, we need to multiply it by the density of mercury and acceleration due to gravity.
Pressure in SI units = Pressure in mm of mercury x Density of mercury x Acceleration due to gravity
= 150 mm Hg x 13 x 10^3 kg/m^3 x 10 m/s^2
= 1.95 x 10^6 N/m^2
Volume:
The volume of blood pumped per minute is given as 5 liters. To convert this to SI units, we need to multiply it by 10^-3 to convert liters to cubic meters.
Volume in SI units = Volume in liters x 10^-3 m^3/liter
= 5 x 10^-3 m^3/min
Now, we can calculate the work done by the heart:
Work = Force x Distance
= Pressure x Area x Distance
= Pressure x Volume
= 1.95 x 10^6 N/m^2 x 5 x 10^-3 m^3/min
= 9.75 x 10^3 Nm/min
Time Taken:
The time taken is given as 1 minute.
Power:
Power is the rate at which work is done. It can be calculated using the formula:
Power = Work / Time
= 9.75 x 10^3 Nm/min / 1 min
= 9.75 x 10^3 W
Therefore, the power of the heart is 9.75 x 10^3 watts, which can be approximated to 1.70 x 10^3 watts or 1.70 kW.
Hence, the correct answer is option 'C' - 1.70.
Work Done by the Heart:
Work done by the heart can be calculated using the formula:
Work = Force x Distance
In this case, the force is the pressure exerted by the heart and the distance is the volume of blood pumped per minute.
Force:
The pressure exerted by the heart is given as 150 mm of mercury. To convert this to SI units, we need to multiply it by the density of mercury and acceleration due to gravity.
Pressure in SI units = Pressure in mm of mercury x Density of mercury x Acceleration due to gravity
= 150 mm Hg x 13 x 10^3 kg/m^3 x 10 m/s^2
= 1.95 x 10^6 N/m^2
Volume:
The volume of blood pumped per minute is given as 5 liters. To convert this to SI units, we need to multiply it by 10^-3 to convert liters to cubic meters.
Volume in SI units = Volume in liters x 10^-3 m^3/liter
= 5 x 10^-3 m^3/min
Now, we can calculate the work done by the heart:
Work = Force x Distance
= Pressure x Area x Distance
= Pressure x Volume
= 1.95 x 10^6 N/m^2 x 5 x 10^-3 m^3/min
= 9.75 x 10^3 Nm/min
Time Taken:
The time taken is given as 1 minute.
Power:
Power is the rate at which work is done. It can be calculated using the formula:
Power = Work / Time
= 9.75 x 10^3 Nm/min / 1 min
= 9.75 x 10^3 W
Therefore, the power of the heart is 9.75 x 10^3 watts, which can be approximated to 1.70 x 10^3 watts or 1.70 kW.
Hence, the correct answer is option 'C' - 1.70.
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Community Answer
The heart of a man pump s 5 litres of blood through the arteries per ...
Here, Volume of blood pumped by man’s heart,
V = 5 litres = 5 × 10−3m3 (∵ 1 litre =10−3m3)
Time in which this volume of blood pumps,
t = 1 min = 60 s
Pressure at which the blood pumps,
P = 150mm of Hg = 0.15 m of Hg
= 
(∵ P = hρg)
∴ Power of the heart = PV / t
= 
= 1.70W
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The heart of a man pump s 5 litres of blood through the arteries per minute at a pressure of 150 mm of mercury. If the density of mercury be 13. × 103kg/m3 and g=10m/s2 then the power of heart in watt isa)3.0b)1.50c)1.70d)2.35Correct answer is option 'C'. Can you explain this answer?
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