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The State of a Gas

The given fig...

Question

The given figure shows the isotherms of a fixed mass of an ideal gas at three temperatures $T_{A}, T_{B}$ and $T_{C}$ then

A

T_{A} > T_{B} > T_{C}

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B

T_{A} < T_{B} < T_{C}

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C

T_{B} < T_{A} < T_{C}

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D

T_{A} = T_{B} = T_{C}

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Solution

The correct option is B $T_{A} < T_{B} < T_{C}$
From the ideal gas equation,
$P V = n R T$
$\Rightarrow \frac{n R T}{V} = P$
By drawing a straight line parallel to $P$ - axis, value of $\frac{1}{V}$ is fixed.
Thus, $P \propto T$

$\Rightarrow P_{C} > P_{B} > P_{A}$
$∴ T_{C} > T_{B} > T_{A}$

OR

From the ideal gas equation,
$P V = n R T$
$\Rightarrow \frac{1}{V} = \frac{P}{n R T}$
Comparing with $y = m x$ ,
$m \propto \frac{1}{T}$
Slope of $A >$ Slope of $B >$ Slope of C
Hence, $T_{C} > T_{B} > T_{A}$

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The State of a Gas

Standard XII Physics

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