The human heart discharges 75ml of blood at each beat against the pressure of 0.1mmHg. Calculate the power of the heart assuming that the purse frequency is 80 beats per minute.(density of mercury is 13.6*10^3 Kg/m3)
1.33 watt
Power P = (13 600 × 9.8 × 0.1 × 10^(-3))(75 × 10^(-6) × 80)/60 = 0.001 332 8 W.
To calculate the power of the heart, we need to know the work done by the heart in a given time period. The formula for power is given by:
Power = Work / Time
First, let's calculate the work done by the heart per beat. The work done is given by:
Work = Force x Distance
The force acting on the blood is the product of pressure and area:
Force = Pressure x Area
The area can be calculated using the formula for the area of a circle:
Area = π x Radius^2
Given that the diameter of a typical human heart is approximately 5 cm, the radius would be 2.5 cm or 0.025 m.
So, the area is:
Area = π x (0.025)^2
Next, we need to calculate the force:
Force = Pressure x Area
Given that the pressure is 0.1 mmHg, we need to convert it to SI units (Pascal). 1 mmHg is equal to 133.3223684 Pascal. So, the pressure is:
Pressure = 0.1 mmHg x 133.3223684 Pascal/mmHg
Now we can calculate the force:
Force = Pressure x Area
Next, we calculate the work done per beat:
Work = Force x Distance
The distance traveled by the blood is the stroke volume, which is given as 75 mL or 0.075 L. We convert it to cubic meters:
Distance = 0.075 L x (1/1000) m^3/L
Now we can calculate the work done per beat:
Work = Force x Distance
To find the power of the heart, we need to know the time period. Given that the heart beats 80 times per minute, we can calculate the time period of one beat:
Time = 60 seconds / 80 beats
Finally, we can calculate the power:
Power = Work / Time
Let's plug in the values and calculate the power.