In each heart beat, a heart pumps 80 ml blood at an average pressure of 100 ml of Hg. What will be the power output of the herat? (Assume 60 heart beat per minute

Options

A. 1.0 W
B. 1.06 W
C. 1.12 W
D. 2.16 W

Answer

To solve the problem of calculating the power output of the heart, we will follow these steps:

### Step 1: Calculate the Work Done by the Heart
The work done (W) by the heart in one minute can be calculated using the formula:
\[ W = P \times \Delta V \]
where:
- \( P \) is the pressure,
- \( \Delta V \) is the change in volume.

### Step 2: Convert the Given Values
1. **Volume per heartbeat**: The heart pumps 80 ml of blood per heartbeat.
- Convert this to cubic meters:
\[ \Delta V = 80 \, \text{ml} = 80 \times 10^{-6} \, \text{m}^3 \]

2. **Pressure**: The average pressure is given as 100 mm of Hg.
- Convert this to Pascals (using the conversion \( 1 \, \text{mm Hg} = 133.322 \, \text{Pa} \)):
\[ P = 100 \, \text{mm Hg} \times 133.322 \, \text{Pa/mm Hg} = 13332.2 \, \text{Pa} \]

### Step 3: Calculate the Total Volume Pumped in One Minute
The heart beats 60 times per minute, so the total volume pumped in one minute is:
\[ \Delta V_{\text{total}} = 60 \, \text{beats/min} \times 80 \times 10^{-6} \, \text{m}^3/beat = 4.8 \times 10^{-3} \, \text{m}^3 \]

### Step 4: Calculate the Work Done in One Minute
Now, substituting the values into the work done formula:
\[ W = P \times \Delta V_{\text{total}} = 13332.2 \, \text{Pa} \times 4.8 \times 10^{-3} \, \text{m}^3 \]
Calculating this gives:
\[ W = 64.0 \, \text{J} \]

### Step 5: Calculate the Power Output
Power (P) is defined as work done per unit time:
\[ P = \frac{W}{t} \]
where \( t = 60 \, \text{s} \) (since we calculated work done in one minute):
\[ P = \frac{64.0 \, \text{J}}{60 \, \text{s}} \approx 1.067 \, \text{W} \]

### Final Answer
Thus, the power output of the heart is approximately:
\[ \text{Power Output} \approx 1.06 \, \text{W} \]