For a fixed mass of an ideal gas held under isothermal conditions, a graph of pressure (P)… — JAMB UTME

For a fixed mass of an ideal gas held under isothermal conditions, a graph of pressure ( $P$ ) plotted against inverse volume ( $\frac{1}{V}$ ) forms a straight line passing through the origin, whose slope increases proportionally with an increase in the system's absolute temperature.

Answer: Answer

Answer

The statement is true because the mathematical formulation of Boyle's Law extended by the ideal gas relation,

P = (nRT)\left(\frac{1}{V}\right)

, matches the linear equation

y = mx

where the slope

m = nRT

is directly proportional to the absolute temperature

T

The statement accurately reflects the mathematical structure of Boyle's Law under ideal gas behavior. Expressing pressure as

P = (nRT)\left(\frac{1}{V}\right)

shows that a plot of

P

versus

\frac{1}{V}

yields a straight line with y-intercept at zero and slope equal to

nRT

. Because the slope is directly proportional to absolute temperature

T

, raising the temperature increases the gradient of the resulting line.

Step-by-Step Solution

Express Boyle's Law incorporating absolute temperature

PV = nRT \implies P = (nRT)\left(\frac{1}{V}\right)

Relate pressure, volume, and absolute temperature mathematically for a fixed mass of gas.

Compare the equation to the standard straight-line equation

y = mx + c

y = P

x = \frac{1}{V}

, slope

m = nRT

, and y-intercept

c = 0

Determine the graphical relationship when

P

is plotted against

\frac{1}{V}

Analyze the dependence of the slope on absolute temperature

Since

n

(moles of gas) and

R

(molar gas constant) are fixed,

m \propto T

Evaluate how increasing absolute temperature affects the gradient of the isotherm.

Key Concept

Boyle's Law Graphical Representation and Slope-Temperature Relationship

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