Which one of the following plots will be a parabola at constant temperature?

Options

A. `Pvs(1)/(V)`
B. PV vs P
C. V vs P
D. none of these

Explanation

To determine which plot will be a parabola at constant temperature, we need to analyze the relationships between pressure (P) and volume (V) based on the ideal gas law and Boyle's law.

### Step-by-Step Solution:

1. **Understand Boyle's Law**: Boyle's law states that at constant temperature, the pressure of a gas is inversely proportional to its volume. Mathematically, this can be expressed as:
\[ P \propto \frac{1}{V} \]
or
\[ PV = k \]
where \( k \) is a constant.

2. **Analyze the Given Options**: We need to evaluate the different plots provided in the options to see which one represents a parabolic relationship.

3. **Option A: P vs 1/V**:
- If we plot pressure (P) against the reciprocal of volume (1/V), we can express it as:
\[ P = k \cdot \left(\frac{1}{V}\right) \]
- This is a linear relationship, which means the graph will be a straight line passing through the origin. **Not a parabola.**

4. **Option B: PV vs P**:
- Here, we have \( PV = k \), which means that the product of pressure and volume is constant. If we plot PV against P, it will also yield a constant value. **Not a parabola.**

5. **Option C: V vs P**:
- If we plot volume (V) against pressure (P), we can rearrange Boyle's law to:
\[ V = \frac{k}{P} \]
- This represents a hyperbolic relationship, not a parabola. **Not a parabola.**

6. **Option D: None of the above**:
- Since none of the previous options yield a parabolic plot, the correct answer is that none of the provided options represent a parabola at constant temperature.

### Conclusion:
The answer is **D: None of these**, as none of the plots given in the options results in a parabolic shape.