Question

Choose the correct option for graphical representation of Boyle’s law, which shows a graph of pressure vs. volume of a gas at different temperatures

• A.
• B.
• C.
• D.

Answer 1

The Correct Option is A

Boyle's law is a fundamental principle of gas behavior that describes the relationship between the pressure and volume of a gas at constant temperature. The law states that the pressure of a given mass of gas is inversely proportional to its volume, provided the temperature remains constant. Mathematically, it can be expressed as:

\(P \propto \frac{1}{V}\) or \(PV = k\)

where:

• \(P\) is the pressure of the gas
• \(V\) is the volume of the gas
• \(k\) is a constant for a given mass and temperature

For the graphical representation of Boyle’s law, we plot pressure (\(P\)) against volume (\(V\)). According to Boyle’s law, this relationship is a hyperbolic curve when the graph is plotted for \(P\) vs. \(V\) of a gas at different constant temperatures, also known as isotherms. As the volume increases, the pressure decreases, resulting in a curve that slopes downward.

The correct graphical representation of this law would show multiple hyperbolic curves on a graph, each representing a different temperature. The graph option provided that correctly represents this relationship is:

This option shows a series of hyperbolic curves, illustrating that for different temperatures, the product \(PV\) is constant, but the curves shift slightly as temperature varies.

In conclusion, the graphical representation of Boyle's law as shown in the first option correctly depicts the inverse relationship between pressure and volume for various temperatures, which is characteristic of this gas law.