During each heartbeat, approximately 71 cm3 of blood is pushed from the heart at an average pressure of 105 mm-Hg. Calculate the power output of the heart, in watts, assuming 68 beats per minute.
The work required per beat is
W = V*deltaP, where V is the volume pumped and delta p is the pressure increase provided. To get that in Joules, V must be in m^3 and deltaP must be in Pascals.
W = 71*10^-6 m^3*(105/760)*1.01*10^5 Pa
= 0.99 J
divide that by the time between beats, (60 sec/min)/(68 beat/min)= 0.88 s
The result is 0.99/0.88 = 1.13 Watts
To calculate the power output of the heart, we can use the formula:
Power = Work / Time
First, let's calculate the work done by the heart per minute. We know that 71 cm3 (cubic centimeters) of blood is pushed per heartbeat, and there are 68 beats per minute. Therefore, the total volume of blood pushed per minute is:
Volume of blood pushed per minute = 71 cm3/beat * 68 beats/minute
Next, we need to convert the volume from cubic centimeters to liters, as the pressure is given in millimeters of mercury. There are 1000 cm3 in a liter, so:
Volume of blood pushed per minute = (71 cm3/beat * 68 beats/minute) / 1000 cm3/L
Now, let's calculate the work done by the heart per minute. The work is equal to the pressure multiplied by the volume of blood pushed per minute. The pressure is given as 105 mm-Hg (millimeters of mercury), which can be converted to Pascal by multiplying by 133.32 Pa/mm-Hg:
Work done per minute = (105 mm-Hg * 133.32 Pa/mm-Hg) * (Volume of blood pushed per minute)
Finally, we can calculate the power output by dividing the work done per minute by the time, which is 60 seconds:
Power output = Work done per minute / 60 seconds
Now we can calculate the power output of the heart in watts. Remember to convert the units properly:
Power output (in watts) = (Work done per minute / 60 seconds) / 1 watt
By plugging in the values, we can solve for the power output.
To calculate the power output of the heart, we need to know the amount of work done by the heart per unit time. Power is defined as the rate at which work is done.
To find the work done by the heart, we can use the formula:
Work = Force x Distance
In this case, force is the pressure exerted by the heart (105 mm-Hg) and distance is the volume of blood pushed out per heartbeat (71 cm3).
Now, let's convert the units to the International System of Units (SI units) before we proceed with the calculation.
1 mm-Hg = 133.322 Pa (Pascals)
1 cm3 = 1 × 10^(-6) m3 (cubic meters)
Therefore, the pressure becomes: 105 mm-Hg x 133.322 Pa/mm-Hg ≈ 13985 Pa
And the volume becomes: 71 cm3 x 1 × 10^(-6) m3/cm3 ≈ 7.1 × 10^(-5) m3
Now, we can determine the work done per heartbeat:
Work = Force x Distance = (13985 Pa) x (7.1 × 10^(-5) m3)
Next, we need to determine the work done per minute by multiplying the work per heartbeat by the beats per minute:
Work per minute = Work per heartbeat x beats per minute
Work per minute = (13985 Pa x 7.1 × 10^(-5) m3) x 68 beats/minute
Finally, to find the power output, which is the rate at which work is done, we divide the work per minute by the time:
Power = Work per minute / time
The time is given in minutes, but we need to convert it to seconds to get the power output in watts. There are 60 seconds in a minute.
Therefore, the power output of the heart can be calculated as follows:
Power = (13985 Pa x 7.1 × 10^(-5) m3) x 68 beats/minute / (60 seconds/minute)
Performing the calculations:
Power = (13985 Pa x 7.1 × 10^(-5) m3) x 68 beats/minute / (60 seconds/minute)
= 6.4867 watts
Therefore, the power output of the heart is approximately 6.4867 watts.