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Home  >>  JEEMAIN and NEET  >>  Physics  >>  Class11  >>  Kinetic Theory of Gases

A student conducted an experiment and found that an ideal gas obeys the condition $\large\frac{p^2}{\rho} = $ constant. Initially the gas is at a temperature $T$, pressure $p$ and density $\rho$. The gas expands such that the density changes to $\rho/2$, which of the following is true?

$(A): $ the pressure of the gas changes to $\sqrt (2p)$ $(B): $ the pressure of the gas is unchanged $(C): $ the graph of the above process on the P-T graph is a parabola $(D): $ the graph of the above process on the P-T graph is a hyperbola

1 Answer

Since $\rho = \large\frac{PM}{RT}$ (where $M$ is the molecular mass of the gas),
Since it's given that $\large\frac{p^2}{\rho} = $ constant, it follows that $\large\frac{p^2}{\frac{PM}{RT}} =$ constant.
$\Rightarrow PT = $ constant.
$\Rightarrow$ the graph is a hyperbola.
answered Jan 22, 2014 by balaji.thirumalai
 

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