Examkin

Question

Difficulty: MediumBoyle's Law and Pressure-Volume Relationship

For a fixed mass of gas maintained at a constant temperature, a plot of pressure (PP) against volume (VV) produces a straight line passing through the origin.

Answer: Answer

Answer

The statement is False. At constant temperature, gas pressure is inversely proportional to volume (P∝1VP \propto \frac{1}{V}), resulting in a hyperbolic curve when plotting PP versus VV, rather than a straight line.
Boyle's law dictates that the pressure of a fixed mass of gas is inversely proportional to its volume at constant temperature (P∝1VP \propto \frac{1}{V}). As a result, graphing pressure (PP) directly against volume (VV) produces a non-linear, downward-sloping curve known as a rectangular hyperbola. To produce a straight line passing through the origin, pressure (PP) must be plotted against the reciprocal of volume (1V\frac{1}{V}).

Step-by-Step Solution

1
State the mathematical formulation of Boyle's law for a fixed mass of gas at constant temperature.
P∝1VP \propto \frac{1}{V} or P⋅V=kP \cdot V = k, where kk is a constant.
Boyle's law describes an inverse relationship between pressure and volume.
2
Analyze the nature of a graph where one variable is plotted directly against another inversely proportional variable (PP vs VV).
The resulting curve is a rectangular hyperbola that approaches the axes asymptotically.
Inversely proportional quantities do not produce a linear plot when graphed directly against each other.
3
Determine the graphical condition required to obtain a straight line passing through the origin.
Plotting pressure (PP) against reciprocal volume (1V\frac{1}{V}) yields a straight line with slope equal to constant kk.
Linearity is achieved by plotting one variable against the reciprocal of the other when P∝1VP \propto \frac{1}{V}.

Key Concept

Graphical representation of Boyle's Law (PP-VV relationship)
Rate this question

Topics

Boyle's Law and Pressure-Volume Relationship

More questions from this topic