Concept:According to Boyle's law, at a constant temperature, the volume (V) of a fixed mass of gas is inversely proportional to its pressure (P). This relationship is expressed as \( V = \frac{k}{P} \).
Solution:- The mathematical equation \( y = \frac{k}{x} \) represents a rectangular hyperbola.
- When we plot Volume (y-axis) against Pressure (x-axis), the resulting graph is a smooth, downward-sloping curve that never touches the axes (an asymptote).
- Because it is a curve, the relationship plotted this way is distinctly non-linear.
- This specific curve at constant temperature is referred to in thermodynamics as an "isotherm".
Why other options are incorrect:- Option A: A straight line would imply a direct proportion (like Charles's law: V vs T).
- Options B & C: The relationship is purely hyperbolic throughout; it does not switch behavior midway.
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