The figure shows graphs of pressure (P) versu | vedclass

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(A) The ideal gas equation is given by $PV = nRT$.Since $n = \frac{m}{M}$ and density $\rho = \frac{m}{V}$,we can write $V = \frac{m}{\rho}$.Substitut

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$T_1 > T_2$

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(A) The ideal gas equation is given by $PV = nRT$.Since $n = \frac{m}{M}$ and density $\rho = \frac{m}{V}$,we can write $V = \frac{m}{\rho}$.Substituting this into the ideal gas equation: $P \left( \frac{m}{\rho} \right) = \left( \frac{m}{M} \right) RT$.Simplifying,we get $P = \left( \frac{RT}{M} \right) \rho$.This equation represents a straight line passing through the origin,$P = m' \rho$,where the slope $m' = \frac{RT}{M}$.Since the slope is directly proportional to temperature $T$ (for a given gas,$R$ and $M$ are constant),the line with the greater slope corresponds to the higher temperature.In the given graph,the slope of the line for $T_1$ is greater than the slope of the line for $T_2$.Therefore,$T_1 > T_2$.

The figure shows graphs of pressure $(P)$ versus density $(\rho)$ for an ideal gas at two temperatures $T_1$ and $T_2$.

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