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(D) According to the ideal gas equation:$P V = n R T$Since the volume $V$ is constant for each vessel,we can write:$P = \left( \frac{n R}{V} \right) T

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linear with different slopes

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(D) According to the ideal gas equation:$P V = n R T$Since the volume $V$ is constant for each vessel,we can write:$P = \left( \frac{n R}{V} \right) T$This equation is of the form $y = m x$,where $y = P$,$x = T$,and the slope $m = \frac{n R}{V}$.Since the mass is given,$n$ is constant. However,the volumes $V$ of the small and large vessels are different.Therefore,the slope $m = \frac{n R}{V}$ will be different for the two vessels.Thus,the $P-T$ curves are linear,passing through the origin,but with different slopes.

$A$ perfect gas of a given mass is heated first in a small vessel and then in a large vessel,such that their volumes remain unchanged. The $P-T$ curves are

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