Volume (V) versus temperature (T) graph of samples of an ideal gas is plotted as shown in figure. Choose the correct alternative. The sample have same number of moles but may have different pressures. If $P_{1}, P_{2}, P_{3}$ and $P_{4}$ are pressures at different states 1, 2, 3 and 4 respectively as shown, then the relation between them is

P_{1} = P_{2} = P_{3} = P_{4}

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P_{1} = P_{2} > P_{3} = P_{4}

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P_{3} = P_{4} > P_{1} = P_{2}

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P_{1} = P_{3} > P_{2} = P_{4}

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Solution

The correct option is C $P_{3} = P_{4} > P_{1} = P_{2}$
$\begin{matrix} p v = n R T v = (\frac{n R}{p}) T P_{3} = p_{4} a n d, p_{1} = p_{2} s l o p e o f 12 i s l e s s t h a n t h a t o f 34 m e a n s \frac{n R}{p_{12}} < \frac{n R}{p_{34}} p_{34} > p_{12} p_{3} = p_{4} > p_{1} = p_{2} \end{matrix}$

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The correct option is C P3=P4>P1=P2pv=nRTv=(nRp)TP3=p4and,p1=p2slopeof12islessthanthatof34meansnRp12<nRp34p34>p12p3=p4>p1=p2