Statement (I): Gas thermometers are less sens | vedclass

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(C) Statement $(I)$ is false because gas thermometers are more sensitive than liquid thermometers due to the higher coefficient of thermal expansion o

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Statements $II, III$ are true, but statement $I$ is false.

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(C) Statement $(I)$ is false because gas thermometers are more sensitive than liquid thermometers due to the higher coefficient of thermal expansion of gases.Statement $(II)$ is true. Boltzmann's constant $k_B$ is defined as the ratio of the universal gas constant $R$ to Avogadro's number $N_A$, i.e.,$k_B = \frac{R}{N_A}$.Statement $(III)$ is true. From the ideal gas equation $PV = nRT$, we have $PV = \frac{m}{M}RT$, where $m$ is mass and $M$ is molar mass. Since density $\rho = \frac{m}{V}$, we get $P = \frac{\rho RT}{M}$. At constant pressure $P$, $\rho \propto \frac{1}{T}$.Therefore, statements $(II)$ and $(III)$ are true, but statement $(I)$ is false.

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