The heart of a man pumps 5 liters of blood through the arteries per minute at a pressure of 150 mm of mercury. If the density of mercury be `13.6xx10^(3) kg//m^(3)` and `g=10 m//s^(2)` then the power of heat in watt is :

Options

A. 1.7
B. 2.35
C. 3
D. 1.5

Explanation

To solve the problem, we need to calculate the power of the heart in watts based on the given parameters. Here’s a step-by-step breakdown:

### Step 1: Convert the volume of blood pumped per minute to cubic meters per second
The heart pumps 5 liters of blood per minute. We need to convert this to cubic meters per second.

\[ \text{Volume per minute} = 5 \text{ liters} = 5 \times 10^{-3} \text{ m}^3 \]

Since there are 60 seconds in a minute, we divide by 60 to convert to cubic meters per second:

\[ \frac{dV}{dt} = \frac{5 \times 10^{-3} \text{ m}^3}{60 \text{ s}} = \frac{5}{60} \times 10^{-3} \text{ m}^3/\text{s} = \frac{1}{12} \times 10^{-3} \text{ m}^3/\text{s} \approx 8.33 \times 10^{-5} \text{ m}^3/\text{s} \]

### Step 2: Convert the pressure from mm of mercury to pascals
The pressure is given as 150 mm of mercury. We need to convert this to pascals (Pa).

Using the formula:

\[ P = \rho g h \]

Where:
- \(\rho\) (density of mercury) = \(13.6 \times 10^3 \text{ kg/m}^3\)
- \(g\) (acceleration due to gravity) = \(10 \text{ m/s}^2\)
- \(h\) (height in meters) = \(150 \text{ mm} = 0.15 \text{ m}\)

Calculating the pressure:

\[ P = 13.6 \times 10^3 \text{ kg/m}^3 \times 10 \text{ m/s}^2 \times 0.15 \text{ m} = 20400 \text{ Pa} \]

### Step 3: Calculate the power of the heart
Power can be calculated using the formula:

\[ \text{Power} = P \times \frac{dV}{dt} \]

Substituting the values we have:

\[ \text{Power} = 20400 \text{ Pa} \times 8.33 \times 10^{-5} \text{ m}^3/\text{s} \]

Calculating the power:

\[ \text{Power} = 20400 \times 8.33 \times 10^{-5} \approx 1.70 \text{ W} \]

### Final Answer
The power of the heart is approximately **1.70 watts**.

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