To find the power of the human heart, we can follow these steps:
### Step 1: Convert the given quantities to appropriate units
- The volume of blood pumped by the heart is given as 4 liters per minute. We need to convert this to cubic meters per second:
\[
\text{Volume} = 4 \, \text{liters} = 4 \times 10^{-3} \, \text{m}^3
\]
Since this is per minute, we convert minutes to seconds:
\[
\text{Volume per second} = \frac{4 \times 10^{-3}}{60} \, \text{m}^3/\text{s} = \frac{4}{60} \times 10^{-3} \, \text{m}^3/\text{s} = \frac{1}{15} \times 10^{-3} \, \text{m}^3/\text{s}
\]
### Step 2: Convert pressure from mm to Pascals
- The pressure is given as 125 mm of mercury. We need to convert this to Pascals (Pa):
\[
\text{Pressure} = 125 \, \text{mm} = 125 \times 10^{-3} \, \text{m}
\]
The pressure in Pascals can be calculated using the formula:
\[
P = \rho g h
\]
where:
- \(\rho\) (density of blood) = \(1.03 \times 10^3 \, \text{kg/m}^3\)
- \(g\) (acceleration due to gravity) = \(10 \, \text{m/s}^2\)
- \(h\) = \(125 \times 10^{-3} \, \text{m}\)
Substituting the values:
\[
P = (1.03 \times 10^3) \times (10) \times (125 \times 10^{-3}) = 1287.5 \, \text{Pa}
\]
### Step 3: Calculate the power of the heart
- The power can be calculated using the formula:
\[
\text{Power} = \frac{\text{Pressure} \times \text{Volume}}{\text{Time}}
\]
Substituting the values:
\[
\text{Power} = \frac{1287.5 \, \text{Pa} \times (4 \times 10^{-3} \, \text{m}^3)}{60 \, \text{s}} = \frac{1287.5 \times 4 \times 10^{-3}}{60}
\]
\[
\text{Power} = \frac{5.15}{60} = 0.0858 \, \text{W}
\]
### Step 4: Convert power to horsepower
- To convert watts to horsepower, we use the conversion factor \(1 \, \text{hp} = 760 \, \text{W}\):
\[
\text{Power in hp} = \frac{0.0858}{760} \approx 0.0001129 \, \text{hp}
\]
This can also be expressed as:
\[
\text{Power in hp} = 112.9 \times 10^{-6} \, \text{hp}
\]
Thus, the power of the heart is approximately \(112.9 \times 10^{-6} \, \text{hp}\).
