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Question

Physics Question on kinetic theory

At constant pressure, which of the following is true ?

A

c∝ρc \propto \sqrt \rho

B

c∝1ρ c \propto \frac{1}{\rho}

C

c∝ρc \propto \rho

D

c∝1ρ c \propto \frac{1}{ \sqrt \rho}

Answer

c∝1ρ c \propto \frac{1}{ \sqrt \rho}

Explanation

Solution

Pressure due to an ideal gas is given by
p = M3Vc2 \frac{ M}{ 3 V} c^2
Putting MV=ρ \frac{M}{ V} = \rho, the density of gas.
p = 13ρc2⇒c=(3 pρ)\frac{ 1}{ 3} \rho c^2 \Rightarrow c = \sqrt{ \bigg( \frac{ 3 \, p}{ \rho} \bigg)}
∴c∝1ρ\therefore c \propto \frac{1}{ \sqrt \rho}