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

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(D) The ideal gas equation is given by $PV = nRT$,where $n = \frac{m}{M}$ ($m$ is the mass,$M$ is the molar mass).Thus,$V = \left(\frac{m}{PM}\right)

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$A$

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(D) The ideal gas equation is given by $PV = nRT$,where $n = \frac{m}{M}$ ($m$ is the mass,$M$ is the molar mass).Thus,$V = \left(\frac{m}{PM}ight) RT$.The slope of the $V-T$ graph is $S = \frac{mR}{PM}$.For the first case (line $D$): $S_1 = \frac{mR}{PM}$. From the graph,the slope of line $D$ is $2$.For the second case (mass $2m$,pressure $P/2$): $S_2 = \frac{(2m)R}{(P/2)M} = 4 \left(\frac{mR}{PM}ight) = 4S_1$.Since $S_1 = 2$,we have $S_2 = 4 	imes 2 = 8$.Looking at the graph,the line with a slope of $8$ is $A$.

The expansion of an ideal gas of mass $m$ at a constant pressure $P$ is given by the straight line $D$. Then the expansion of the same ideal gas of mass $2m$ at a pressure $P/2$ is given by the straight line

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