The pressure versus temperature graph of an i | vedclass

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(A) For an ideal gas,the equation of state is $PV = nRT$,which can be written as $P = (nR/V)T$.Comparing this with the equation of a straight line $y

Vedclass · Accepted Answer

$V_1 = V_2, V_3 = V_4$ and $V_2 > V_3$

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(A) For an ideal gas,the equation of state is $PV = nRT$,which can be written as $P = (nR/V)T$.Comparing this with the equation of a straight line $y = mx$,where $y = P$ and $x = T$,the slope $m = nR/V$.Since the number of moles $n$ is constant,the slope $m$ is inversely proportional to the volume $V$ $(m \propto 1/V)$.In the given graph,lines $1$ and $2$ have the same slope,and lines $3$ and $4$ have the same slope.Therefore,$V_1 = V_2$ and $V_3 = V_4$.Since the slope of lines $3$ and $4$ is greater than the slope of lines $1$ and $2$,and slope is inversely proportional to volume,the volume corresponding to lines $3$ and $4$ must be smaller than the volume corresponding to lines $1$ and $2$.Thus,$V_2 > V_3$.

The pressure versus temperature graph of an ideal gas for equal number of moles at different volumes is plotted as shown in the figure. Choose the correct alternative.

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