Which of the following statement(s) is (are) | vedclass

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(A) $U_{rms} = \sqrt{\frac{3RT}{M}}$. Since $U_{rms} \propto \sqrt{T}$,if $T$ becomes $4T$,$U_{rms}$ becomes $\sqrt{4} = 2$ times. Thus,statement $(1)

Vedclass · Accepted Answer

$(1), (2), (3)$

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(A) $U_{rms} = \sqrt{\frac{3RT}{M}}$. Since $U_{rms} \propto \sqrt{T}$,if $T$ becomes $4T$,$U_{rms}$ becomes $\sqrt{4} = 2$ times. Thus,statement $(1)$ is correct.$\varepsilon_{av} = \frac{3}{2}kT$. This expression depends only on temperature $T$ and not on molecular mass $M$. Thus,statement $(2)$ is correct.From $U_{rms} = \sqrt{\frac{3RT}{M}}$,$U_{rms} \propto \frac{1}{\sqrt{M}}$. Thus,statement $(3)$ is correct.Since $\varepsilon_{av} = \frac{3}{2}kT$,$\varepsilon_{av} \propto T$. If $T$ is increased four times,$\varepsilon_{av}$ increases four times,not doubled. Thus,statement $(4)$ is incorrect.Therefore,statements $(1), (2),$ and $(3)$ are correct.

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