When the pressure remains constant, the mean free path of a gas varies with absolute temperature as\

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$ \quad \lambda=\frac{1}{\sqrt{2} \pi \sigma^{2} \mathrm{n}}$\ where $\lambda=$ mean free path ie the average distance between two collisions\ $\sigma=$ molecular diameter\ $\mathrm{n}=$ number of molecules per unit volume\ But $\mathrm{P}=\frac{1}{3} \mathrm{nmc}^{2} \quad \mathrm{n}=\frac{3 \mathrm{P}}{\mathrm{mc}^{2}}$\ $	herefore \lambda=\frac{1}{\sqrt{2} \pi \sigma^{2} \frac{3 \mathrm{P}}{\mathrm{mc}^{2}}}=\frac{\mathrm{mc}^{2}}{\sqrt{2} \pi \sigma^{2} 3 \mathrm{P}}$\ Case 1:-\ Temperature remains constant and pressure changes. Then $\mathrm{m} \overline{\mathrm{c}}^{2}$ is constant\ $	herefore \lambda \propto \frac{1}{\mathrm{P}}$\ Case 2:-\ Volume remains constant and temperature changes. Then $\mathrm{P} \propto \mathrm{T}, \mathrm{mc}^{2} \propto \mathrm{~T}$\ $	herefore \lambda$ is independent of temperature\ Case 3:-\ Pressure remains constant and temperature changes. Then $\mathrm{mc}^{2} \propto \mathrm{~T}, 	herefore \lambda \propto \mathrm{~T}$\