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  • Using the equation of state pV= nRT; show that at a given temperature density of a gas is proportional to gas pressure p.

5.3  Using the equation of state pV=nRT; show that at a given temperature density of a gas is proportional to gas pressure p.

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Given ideal gas equation ;

PV = nRT

So, at given fixed temperature T. we have the

Density\ of\ gas (\rho ) = \frac{mass(m)}{Volume(V)}

And we know n = \frac{Mass\ of\ gas}{Molar\ mass\ of\ gas}

so, we get P = \frac{mRT}{MV}  

P = \frac{\rho RT}{M}

But at constant Temperature, we have P \propto \rho.

Posted by

Divya Prakash Singh

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