If the heart pushes 1 cc of blood in one second under pressure 20000 N/m 2 the power of heart is

Options

A. 0.02 W
B. 400 W
C. `5xx10` W
D. 0.2 W

Answer

To find the power of the heart when it pushes 1 cc (cubic centimeter) of blood in one second under a pressure of 20,000 N/m², we can follow these steps:

### Step 1: Understand the relationship between pressure, force, and area
Pressure (P) is defined as force (F) per unit area (A). Therefore, we can express the force as:
\[ F = P \times A \]

### Step 2: Convert volume to cubic meters
1 cc (cubic centimeter) is equivalent to \( 1 \times 10^{-6} \) cubic meters.

### Step 3: Calculate the area
Since the heart pushes 1 cc of blood in one second, we can relate the volume to the area and the distance (height) the blood is pushed.
Let’s denote the distance the blood is pushed in one second as \( d \). The volume can be expressed as:
\[ V = A \times d \]
Given that \( V = 1 \times 10^{-6} \) m³ and \( d = v \times t \) (where \( t = 1 \) second), we can write:
\[ 1 \times 10^{-6} = A \times v \]

### Step 4: Relate velocity to pressure and force
The power (P) can also be expressed as:
\[ P = F \times v \]
Substituting the expression for force from Step 1:
\[ P = (P \times A) \times v \]
This simplifies to:
\[ P = P \times A \times v \]

### Step 5: Substitute for area using volume
From Step 3, we have:
\[ A = \frac{1 \times 10^{-6}}{v} \]
Substituting this into the power equation gives:
\[ P = P \times \left(\frac{1 \times 10^{-6}}{v}\right) \times v \]
This simplifies to:
\[ P = P \times 1 \times 10^{-6} \]

### Step 6: Calculate the power
Now substituting the given pressure (20,000 N/m²):
\[ P = 20000 \times 1 \times 10^{-6} \]
\[ P = 0.02 \text{ Watts} \]

### Final Answer
The power of the heart is **0.02 Watts**.

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