Easy
On any planet,the presence of an atmosphere implies ($C_{rms}$ = root mean square velocity of molecules and $V_e$ = escape velocity):
- A$C_{rms} << V_e$
- B$C_{rms} > V_e$
- C$C_{rms} = V_e$
- D$C_{rms} = 0$
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The average speed $\bar{v}$ and $r.m.s.$ speed $v_{rms}$ of the molecules are related as
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View SolutionIf ${V_H}$,${V_N}$,and ${V_O}$ denote the root-mean-square velocities of molecules of hydrogen,nitrogen,and oxygen respectively at a given temperature,then:
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View SolutionThe temperature of a gas is $-50^{\circ}C$. To what temperature should the gas be heated so that the $rms$ speed is increased by $3$ times?
Column-$I$ represents the formula for ${v_{rms}}$ and Column-$II$ represents the corresponding condition (phenomena). Match them correctly:
Column-$I$ Column-$II$ $(a)$ ${v_{rms}} = \sqrt {\frac{3P}{\rho}}$ $(i)$ For $1 \text{ mole ideal gas}$ $(b)$ ${v_{rms}} = \sqrt {\frac{3RT}{M_0}}$ $(ii)$ For one molecule of gas $(c)$ ${v_{rms}} = \sqrt {\frac{3{k_B}T}{m}}$ $(iii)$ On the basis of kinetic theory
| Column-$I$ | Column-$II$ |
| $(a)$ ${v_{rms}} = \sqrt {\frac{3P}{\rho}}$ | $(i)$ For $1 \text{ mole ideal gas}$ |
| $(b)$ ${v_{rms}} = \sqrt {\frac{3RT}{M_0}}$ | $(ii)$ For one molecule of gas |
| $(c)$ ${v_{rms}} = \sqrt {\frac{3{k_B}T}{m}}$ | $(iii)$ On the basis of kinetic theory |
Medium
View SolutionThe respective speeds of the five molecules are $1, 2, 3, 4$ and $5 \ km/s$. The ratio of their root mean square (rms) velocity to their average velocity is:
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