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Kinetic Theory

Question

A graph between pressure P (along with the y-axis) and absolute temperature, T (along with the x-axis) for equal moles of two gases have been drawn. Given that the volume of the second gas is more than the volume of first gas. Which of the following statement is correct?

Slope of gas 1 is less than gas 2

Slope og gas 1 is more than gas 2

Both have some slopes

None of the above

Solution

Slope og gas 1 is more than gas 2

According to the ideal gas equation,

pV = nRT .... (i)

$pV = nRT or \frac{p}{T} = \frac{nR}{V}$

P/T represents the slope of the graph. As the number of moles is the same for the two gases.

$∴ \frac{P}{T} \propto \frac{1}{V} ∵ V_{2} > V_{1} ∴ (slope)_{2} < (slope)_{1}$