Which one of the following plot will be a hyperbola at constant temperature ?

Options

A. P vs 1/V
B. PV vs P
C. V vs P
D. None of these

Explanation

To determine which plot will be a hyperbola at constant temperature, we can follow these steps:

### Step-by-Step Solution:

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

2. **Rearranging the Equation**: From the equation \( PV = k \), we can express pressure in terms of volume:
\[ P = \frac{k}{V} \]
This shows that pressure decreases as volume increases, and vice versa.

3. **Graphical Representation**: If we plot pressure (P) on the y-axis and volume (V) on the x-axis, the relationship \( P = \frac{k}{V} \) will yield a hyperbolic curve. This is because as volume increases, pressure decreases, and the graph will not intersect the axes, which is characteristic of a hyperbola.

4. **Conclusion**: Therefore, the plot of pressure versus volume at constant temperature will be a hyperbola.

### Final Answer:
The plot that will be a hyperbola at constant temperature is the one representing the relationship between pressure (P) and volume (V) according to Boyle's Law.