The heat of a man pumps 5 litres 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. `1.50`
B. `1.70`
C. `2.35`
D. `3.0`

Explanation

To find the power of the heart in watts when pumping blood, we can follow these steps:

### Step 1: Convert the volume of blood from liters to cubic meters
The volume of blood pumped is given as 5 liters. We need to convert this to cubic meters.

\[ V = 5 \, \text{liters} = 5 \times 10^{-3} \, \text{m}^3 \]

### Step 2: Convert the time from minutes to seconds
The time taken to pump this volume is given as 1 minute. We convert this to seconds.

\[ T = 1 \, \text{minute} = 60 \, \text{seconds} \]

### Step 3: Calculate the pressure in pascals
The pressure is given as 150 mm of mercury. We need to convert this to pascals 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 of mercury column) = \(150 \, \text{mm} = 150 \times 10^{-3} \, \text{m}\)

Calculating the pressure:

\[ P = 13.6 \times 10^3 \, \text{kg/m}^3 \times 10 \, \text{m/s}^2 \times 150 \times 10^{-3} \, \text{m} \]

\[ P = 13.6 \times 10^3 \times 10 \times 0.15 = 20400 \, \text{Pa} \]

### Step 4: Calculate the work done
The work done (W) by the heart in pumping the blood can be calculated using the formula:

\[ W = P \times V \]

Substituting the values we have:

\[ W = 20400 \, \text{Pa} \times 5 \times 10^{-3} \, \text{m}^3 \]

\[ W = 102 \, \text{J} \]

### Step 5: Calculate the power
Power (P) is defined as work done per unit time:

\[ P = \frac{W}{T} \]

Substituting the values:

\[ P = \frac{102 \, \text{J}}{60 \, \text{s}} \approx 1.7 \, \text{W} \]

### Final Answer
The power of the heart is approximately **1.7 watts**.

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