Pressure versus temperature graphs of an idea | vedclass

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(C) The density $\rho$ of an ideal gas is given by $\rho = \frac{PM}{RT}$,where $P$ is pressure,$M$ is molar mass,$R$ is the gas constant,and $T$ is t

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Density of gas is constant in graph (iii)

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(C) The density $\rho$ of an ideal gas is given by $\rho = \frac{PM}{RT}$,where $P$ is pressure,$M$ is molar mass,$R$ is the gas constant,and $T$ is temperature.For graph $(i)$: Temperature $T$ is constant,and pressure $P$ is increasing. Since $\rho \propto P$ at constant $T$,the density is increasing. This statement is correct.For graph (ii): Pressure $P$ is constant,and temperature $T$ is increasing. Since $\rho \propto \frac{1}{T}$ at constant $P$,the density is decreasing. This statement is correct.For graph (iii): The graph is a straight line not passing through the origin. The equation is $P = mT + c$. Thus,$\frac{P}{T} = m + \frac{c}{T}$. Since $\rho = \frac{M}{R} \cdot \frac{P}{T}$,the density $\rho = \frac{M}{R} (m + \frac{c}{T})$. As $T$ increases,$\frac{c}{T}$ decreases,so the density $\rho$ is decreasing. Therefore,the statement that density is constant in graph (iii) is wrong.

Pressure versus temperature graphs of an ideal gas are as shown in the figure. Choose the wrong statement.

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