Which of the following curves represent the v | vedclass

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(B) Volume expansion is the expansion of the volume of a gas due to an increase in its temperature.$	herefore$ The coefficient of volume expansion $\

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(B) Volume expansion is the expansion of the volume of a gas due to an increase in its temperature.$	herefore$ The coefficient of volume expansion $\alpha_{V}$ is defined as:$\alpha_{V} = \frac{1}{V} \left( \frac{\partial V}{\partial T} ight)_{p} ... (i)$From the ideal gas equation,$pV = nRT$,we have $V = \frac{nRT}{p}$.Differentiating with respect to $T$ at constant pressure $p$:$\left( \frac{\partial V}{\partial T} ight)_{p} = \frac{nR}{p}$Substituting this into equation $(i)$:$\alpha_{V} = \frac{1}{V} \left( \frac{nR}{p} ight) = \frac{1}{V} \left( \frac{pV}{T} \cdot \frac{1}{p} ight) = \frac{1}{T}$Thus,$\alpha_{V} = \frac{1}{T}$.This implies that $\alpha_{V}$ is directly proportional to $\frac{1}{T}$. Therefore,a graph of $\alpha_{V}$ versus $\frac{1}{T}$ will be a straight line passing through the origin. This is correctly depicted in option $(b)$.

Which of the following curves represent the variation of coefficient of volume expansion of an ideal gas at constant pressure?

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