Medium
At a temperature of $27^{\circ}C$ and a pressure of $1.0 \times 10^5 \, N/m^2$,the $rms$ speed of a gas is $200 \, m/s$. What is the $rms$ speed at a temperature of $127^{\circ}C$ and a pressure of $0.5 \times 10^5 \, N/m^2$?
- A$\frac{100\sqrt{2}}{3} \, m/s$
- B$100\sqrt{2} \, m/s$
- C$\frac{400}{\sqrt{3}} \, m/s$
- DNone of these
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The $r.m.s.$ speed of the molecules of a gas in a vessel is $400 \; m/s$. If half of the gas leaks out,at constant temperature,the $r.m.s.$ speed of the remaining molecules will be ..... $m/s$.
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View Solution$Assertion :$ The root mean square and most probable speeds of the molecules in a gas are the same.
$Reason :$ The Maxwell distribution for the speed of molecules in a gas is symmetrical.
$Reason :$ The Maxwell distribution for the speed of molecules in a gas is symmetrical.
The speed distribution for a sample of $N$ gas particles is shown below. $P(v) = 0$ for $v > 2 v_0$. How many particles have speeds between $1.2 v_0$ and $1.8 v_0$ (in $N$)?
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
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