Q. The speeds of $5$ molecules of a gas (in arbitrary units) are as follows: $2,3,4,5,6$. The root mean square speed for these molecules is

Kinetic Theory Report Error

A

$2.91$

0%

B

$3.52$

27%

C

$4.00$

33%

D

$4.24$

40%

Solution:

$v_{r m s}=\sqrt{\frac{v_{1}^{2}+v_{2}^{2}+v_{3}^{2}+v_{4}^{2}+v_{5}^{2}}{5}}=4.24$

Questions from Kinetic Theory

1. Which one of the following is not an assumption in the kinetic theory of gases?

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2. A gas at one atmosphere and 100 mL is mixed with another gas of equal moles at 0.5 atm and having volume 50 mL in flask of 1 L. What is their final pressure?

3. Two moles of monoatomic gas is mixed with three moles of a diatomic gas. The molar specific heat of the mixture at constant volume is

4. At what temperature is the root mean square speed of an atom in an argon gas cylinder equal to the rms speed of a helium gas atom at -$20\,{}^{\circ}C$ ? (Atomic mass of $Ar = 39 \,u$ and $He = 400 \,u$)

5. In a process, temperature and volume of one mole of an ideal monoatomic gas are varied according to the relation $VT = K$, where $K$ is a constant. In this process the temperature of the gas is incresed by $\Delta T$. The amount of heat absorbed by gas is (R is gas constant) :

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1. If $E$ and $G$ respectively denote energy and gravitational constant, then $\frac{ E }{ G }$ has the dimensions of:

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3. A car starts from rest and accelerates at $5\, m / s ^{2}$ At $t=4\, s$, a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at $t =6\, s$ ? (Take $\left. g =10\, m / s ^{2}\right)$

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4. A wheel with $20$ metallic spokes each $1\, m$ long is rotated with a speed of $120\, rpm$ in a plane perpendicular to a magnetic field of $0.4\, G$. The induced emf between the axle and rim of the wheel will be, $(1 G = 10^{-4}\, T)$

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5. A barometer is constructed using a liquid (density $= 760 \,kg/m^{3})$ What would be the height of the liquid column, when a mercury barometer reads $76\, cm$ ?
(density of mercury $= 13600 kg/m^{3})$

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