The expansion of an ideal gas of mass m at a | vedclass

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Question

(C) From the ideal gas equation,$PV = nRT$,where $n = \frac{m}{M}$ ($M$ is the molar mass).At constant pressure $P$,the equation becomes $V = \left(\f

Vedclass · Accepted Answer

$B$

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(C) From the ideal gas equation,$PV = nRT$,where $n = \frac{m}{M}$ ($M$ is the molar mass).At constant pressure $P$,the equation becomes $V = \left(\frac{mR}{MP}\right)T$.The slope of the $V-T$ graph is given by $S = \frac{mR}{MP}$.In the first case,the slope is $S_1 = \frac{mR}{MP}$.In the second case,the mass is $2m$ and the pressure is $2P$. The new slope $S_2$ is:$S_2 = \frac{(2m)R}{M(2P)} = \frac{mR}{MP} = S_1$.Since the slope remains the same,the expansion of the gas will be represented by the same straight line $B$.Therefore,the correct option is $C$.

The expansion of an ideal gas of mass $m$ at a constant pressure $P$ is given by the straight line $B$ in the $V-T$ graph. Then the expansion of the same ideal gas of mass $2m$ at a pressure $2P$ is given by the straight line:

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