Which is the true graphical representation of V vs 1/P

Options

A.
B.
C.
D.

Answer

To solve the question of finding the true graphical representation of V vs 1/P, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Relationship**:
According to Boyle's Law, the volume (V) of a gas is inversely proportional to the pressure (P) of the gas. This can be expressed mathematically as:
\[ V \propto \frac{1}{P} \]
This means that as the pressure increases, the volume decreases, and vice versa.

2. **Rearranging the Proportionality**:
From the proportionality, we can express this relationship as:
\[ V = k \cdot \frac{1}{P} \]
where \(k\) is a constant.

3. **Introducing a New Variable**:
To analyze the graph of V vs 1/P, we can introduce a new variable:
\[ x = \frac{1}{P} \]
Thus, we can rewrite the equation as:
\[ V = k \cdot x \]

4. **Identify the Type of Graph**:
The equation \(V = k \cdot x\) is in the form of a linear equation \(y = mx\), where:
- \(y\) is the volume (V)
- \(x\) is \(1/P\)
- \(m\) is the constant \(k\)

5. **Graph Characteristics**:
- The graph of V vs 1/P will be a straight line.
- Since the relationship is directly proportional, the line will pass through the origin (0,0).

6. **Conclusion**:
Therefore, the true graphical representation of V vs 1/P is a straight line passing through the origin.

### Final Answer:
The true graphical representation of V vs 1/P is a straight line that passes through the origin.

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