Figure show graphs of pressure vs density for an ideal gas at two temperatures $T_{1}$ and $T_{2}$
What can be inferred about $T_{1}$ and $T_{2}$ ?

T_{1} > T_{2}

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T_{1} = T_{2}

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T_{1} < T_{2}

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any of the three is possible

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Solution

The correct option is A $T_{1} > T_{2}$
Ideal gas equation $\to P V = n R T$
$\Rightarrow P V = n R T$
$\Rightarrow P V = \frac{m R T}{M}$ $m = m a s s o f g a s$
$M = M o l o r m a s s o f a m o l e c u l a r$
$\Rightarrow P \frac{V}{m} = \frac{R T}{M}$

$\Rightarrow \frac{P}{ρ} = \frac{R T}{M}$ [As $ρ = \frac{m}{V}$ ]
$\Rightarrow P = (\frac{R T}{M}) ρ$
So, comparing with $y = m x$
Greater slope for higher temperature.
Hence, the answer is $T_{1} > T_{2} .$

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