During each heart beat, approximately 70cubic cm of blood is from the heart at an average pressure of 105mmHg. Calculate the power output of the heart, in watts, assuming 70 beats per minute.
To calculate the power output of the heart, we need to know the work done by the heart in a given time period. The work done can be calculated by multiplying the force exerted by the heart with the displacement covered during each heartbeat.
Given:
Volume of blood pumped per heartbeat = 70 cubic cm
Pressure at which blood is pumped = 105 mmHg
To calculate the force exerted by the heart, we need to convert the pressure to Pascal (Pa), as the SI unit of pressure is the pascal:
1 mmHg = 133.322 Pa
Therefore, the pressure in pascals would be:
105 mmHg x 133.322 Pa/mmHg = 13,999.61 Pa
Now, let's calculate the displacement in meters covered during each heartbeat. To do this, we need to convert the volume from cubic cm to cubic meters:
1 cm^3 = 0.000001 m^3
Therefore, the volume in cubic meters would be:
70 cm^3 x 0.000001 m^3/cm^3 = 0.00007 m^3
The work done by the heart can be calculated by multiplying the force (pressure) with the displacement:
Work = Force x Displacement
Work = 13,999.61 Pa x 0.00007 m^3 = 0.9799727 J (joules)
Now, we have the work done in joules per heartbeat. To find the power output, we divide the work by the time taken for each heartbeat. Since we are given the heart rate of 70 beats per minute, we need the time taken for each heartbeat in seconds:
1 minute = 60 seconds
Therefore, the time taken for each heartbeat in seconds would be:
60 seconds / 70 beats = 0.8571 seconds/beat
Finally, we can calculate the power output of the heart using the following formula:
Power = Work / Time
Power = 0.9799727 J / 0.8571 s = 1.14239 W (watts)
Therefore, the power output of the heart is approximately 1.14239 watts.