Kinetic Theory of Gases · JEE Main previous year questions

The energy released when $\frac{7}{17.13}\mathrm{kg}$ of ${}_3^7\mathrm{Li}$ is converted into ${}_2^4\mathrm{He}$ by proton bombardment is $\alpha \times 10^{32}\mathrm{eV}$. The value of $\alpha$ is ____. (Nearest integer) (Mass of ${}_3^7\mathrm{Li}=7.0183\mathrm{u}$, mass of ${}_2^4\mathrm{He}=4.004\mathrm{u}$, mass of proton $=1.008\mathrm{u}$ and $1\mathrm{u}=931MeV/{\mathrm{c}}^2$ and Avogadro number $=6.0\times 10^{23}$)

The mean free path of a molecule of diameter $5\times 10^{-10}\text{ m}$ at the temperature $41^{\circ }\text{C}$ and pressure $1.38\times 10^5\text{ Pa}$, is given as ________ m. (Given $k_B=1.38\times 10^{-23}\text{ J/K}$).

1. A.$2\sqrt{2}\times 10^{-10}$
2. B.$10\sqrt{2}\times 10^{-8}$
3. C.$2\sqrt{2}\times 10^{-8}$
4. D.$2\times 10^{-8}$

The volume of an ideal gas increases 8 times and temperature becomes $(1/4{)}^{\text{th}}$ of initial temperature during a reversible change. If there is no exchange of heat in this process $(\Delta \mathrm{Q}=0)$ then identify the gas from the following options (Assuming the gases given in the options are ideal gases) :

1. A.$\mathrm{N}{\mathrm{H}}_3$
2. B.${\mathrm{O}}_2$
3. C.$\mathrm{C}{\mathrm{O}}_2$
4. D.He

The mean free path and the average speed of oxygen molecules at 300 K and 1 atm are $3\times 10^{-7}\mathrm{m}$ and $600m/s$, respectively. Find the frequency of its collisions.

1. A.$5\times 10^8/\mathrm{s}$
2. B.$9\times 10^5/\mathrm{s}$
3. C.$2\times 10^{10}/\mathrm{s}$
4. D.$2\times 10^9/\mathrm{s}$

1. A.
2. B.
3. C.
4. D.

Given below are two statements : Statement (I) : The mean free path of gas molecules is inversely proportional to square of molecular diameter. Statement (II) : Average kinetic energy of gas molecules is directly proportional to absolute temperature of gas. In the light of the above statements, choose the correct answer from the options given below :

1. A.Statement I is false but Statement II is true
2. B.Both Statement I and Statement II are true
3. C.Statement I is true but Statement II is false
4. D.Both Statement I and Statement II are false

Energy of 10 non rigid diatomic molecules at temperature $T$ is :

1. A.$35\mathrm{RT}$
2. B.$\frac{7}{2}\mathrm{RT}$
3. C.$70{\mathrm{K}}_{\mathrm{B}}\mathrm{T}$
4. D.$35{\mathrm{K}}_{\mathrm{B}}\mathrm{T}$

If $n$ is the number density and $d$ is the diameter of the molecule, then the average distance covered by a molecule between two successive collisions (i.e. mean free path) is represented by :

1. A.$\frac{1}{\sqrt{2}n\pi d^2}$
2. B.$\frac{1}{\sqrt{2}{n}^2{\pi }^2{d}^2}$
3. C.$\frac{1}{\sqrt{2n}\pi d^2}$
4. D.$\sqrt{2}n\pi d^2$

1. A.${\rho }_1>{\rho }_2$
2. B.${\rho }_2<{\rho }_3$
3. C.${\rho }_1={\rho }_2={\rho }_3$
4. D.${\rho }_1<{\rho }_2$

The translational degrees of freedom $(f_t)$ and rotational degrees of freedom $(f_r)$ of ${\text{CH}}_4$ molecule are:

1. A.$f_t=2$ and $f_r=2$
2. B.$f_t=3$ and $f_r=3$
3. C.$f_t=3$ and $f_r=2$
4. D.$f_t=2$ and $f_r=3$

$N$ moles of a polyatomic gas ($f=6$) must be mixed with two moles of a monoatomic gas so that the mixture behaves as a diatomic gas. The value of $N$ is :

1. A.6
2. B.2
3. C.4
4. D.3

The average kinetic energy of a monatomic molecule is $0.414\text{ eV}$ at temperature : (Use $K_B=1.38\times 10^{-23}\text{ J/mol}-\text{K}$)

1. A.$3000\text{ K}$
2. B.$3200\text{ K}$
3. C.$1600\text{ K}$
4. D.$1500\text{ K}$

The rms speed of oxygen molecule in a vessel at particular temperature is ${\left(1+\frac{5}{x}\right)}^{\frac{1}{2}}v$, where $v$ is the average speed of the molecule. The value of $x$ will be: ( Take $\pi =\frac{22}{7}$ )

1. A.$4$
2. B.$8$
3. C.$28$
4. D.$27$

The mean free path of molecules of a certain gas at STP is $1500\text{ d}$, where $\mathrm{d}$ is the diameter of the gas molecules. While maintaining the standard pressure, the mean free path of the molecules at $373\text{ K}$ is approximately:

1. A.$750\text{ d}$
2. B.$1500\text{ d}$
3. C.$2049\text{ d}$
4. D.$1098\text{ d}$

Three vessels of equal volume contain gases at the same temperature and pressure. The first vessel contains neon (monoatomic), the second contains chlorine (diatomic) and third contains uranium hexafluoride (polyatomic). Arrange these on the basis of their root mean square speed ($v_{\text{rms}}$) and choose the correct answer from the options given below:

1. A.${\text{v}}_{\text{rms}}(\text{ mono })={\text{v}}_{\text{rms}}(\text{ dia })={\text{v}}_{\text{rms}}(\text{ poly })$
2. B.${\text{v}}_{\text{rms}}(\text{mono})>{\text{v}}_{\text{rms}}(\text{dia})>{\text{v}}_{\text{rms}}(\text{poly})$
3. C.${\text{v}}_{\text{rms}}(\text{dia})<{\text{v}}_{\text{rms}}(\text{poly})<{\text{v}}_{\text{rms}}(\text{mono})$
4. D.${\text{v}}_{\text{rms}}(\text{mono})<{\text{v}}_{\text{rms}}(\text{dia})<{\text{v}}_{\text{rms}}(\text{poly})$

The root mean square speed of molecules of nitrogen gas at $27^{\circ }\mathrm{C}$ is approximately : (Given mass of a nitrogen molecule $=4.6\times 10^{-26}\text{ kg}$ and take Boltzmann constant $k_{\mathrm{B}}=1.4\times 10^{-23}{\text{ J K}}^{-1}$)

1. A.$91\text{ m/s}$
2. B.$1260\text{ m/s}$
3. C.$27.4\text{ m/s}$
4. D.$523\text{ m/s}$

Match List I with List II : $$\begin{array}{llll}& \text{List I}& & \text{List II}\\ \text{(A)}& \text{3 Translational degrees of freedom}& \text{(I)}& \text{Monoatomic gases}\\ \text{(B)}& \text{3 Translational, 2 rotational degrees of freedom}& \text{(III)}& \text{Rigid diatomic gases}\\ \text{(C)}& \text{3 Translational, 2 rotational and 1 vibrational degrees of freedom}& \text{(IV)}& \text{Nonrigid diatomic gases}\\ \text{(D)}& \text{3 Translational, 3 rotational and more than one vibrational degrees of freedom}& \text{(II)}& \text{Polyatomic gases}\end{array}$$ Choose the correct answer from the options given below:

1. A.(A)-(I), (B)-(III), (C)-(IV), (D)-(II)
2. B.(A)-(IV), (B)-(III), (C)-(II), (D)-(I)
3. C.(A)-(IV), (B)-(II), (C)-(I), (D)-(III)
4. D.(A)-(I), (B)-(IV), (C)-(III), (D)-(II)

The temperature of an ideal gas is increased from $200\mathrm{K}$ to $800\mathrm{K}$. If r.m.s. speed of gas at $200\mathrm{K}$ is $v_0$. Then, r.m.s. speed of the gas at $800\mathrm{K}$ will be:

1. A.$v_0$
2. B.$2v_0$
3. C.$4v_0$
4. D.$\frac{v_0}{4}$

At 300 K, the rms speed of oxygen molecules is $\sqrt{\frac{\alpha +5}{\alpha }}$ times to that of its average speed in the gas. Then, the value of $\alpha$ will be (used $\pi =\frac{22}{7}$)

1. A.27
2. B.28
3. C.24
4. D.32

The root mean square velocity of molecules of gas is

1. A.Proportional to temperature $(T)$
2. B.Inversely proportional to square root of temperature $\left(\sqrt{\frac{1}{T}}\right)$
3. C.Proportional to square of temperature $(T^2)$
4. D.Proportional to square root of temperature $(\sqrt{T})$

Given below are two statements : Statement I : The temperature of a gas is $-73^{\circ }\mathrm{C}$. When the gas is heated to $527^{\circ }\mathrm{C}$, the root mean square speed of the molecules is doubled. Statement II : The product of pressure and volume of an ideal gas will be equal to translational kinetic energy of the molecules. In the light of the above statements, choose the correct answer from the options given below :

1. A.Statement I is true but Statement II is false
2. B.Both Statement I and Statement II are true
3. C.Statement I is false but Statement II is true
4. D.Both Statement I and Statement II are false

The root mean square speed of smoke particles of mass $5\times 10^{-17}\mathrm{kg}$ in their Brownian motion in air at NTP is approximately. $[\text{Given }\mathrm{k}=1.38\times 10^{-23}\mathrm{J}{\mathrm{K}}^{-1}]$

1. A.$60\mathrm{mm}{\mathrm{s}}^{-1}$
2. B.$12\mathrm{mm}{\mathrm{s}}^{-1}$
3. C.$15\mathrm{mm}{\mathrm{s}}^{-1}$
4. D.$36\mathrm{mm}{\mathrm{s}}^{-1}$

Given below are two statements : Statement I : The average momentum of a molecule in a sample of an ideal gas depends on temperature. Statement II : The rms speed of oxygen molecules in a gas is $v$. If the temperature is doubled and the oxygen molecules dissociate into oxygen atoms, the rms speed will become $2v$. In the light of the above statements, choose the correct answer from the options given below :

1. A.Both Statement I and Statement II are true
2. B.Both Statement I and Statement II are false
3. C.Statement I is true but Statement II is false
4. D.Statement I is false but Statement II is true

At a certain temperature, the degrees of freedom per molecule for gas is 8. The gas performs 150 J of work when it expands under constant pressure. The amount of heat absorbed by the gas will be _________ J.

Which statements are correct about degrees of freedom ? (A) A molecule with $\mathrm{n}$ degrees of freedom has ${\mathrm{n}}^2$ different ways of storing energy. (B) Each degree of freedom is associated with $\frac{1}{2}\mathrm{RT}$ average energy per mole. (C) A monatomic gas molecule has 1 rotational degree of freedom whereas diatomic molecule has 2 rotational degrees of freedom. (D) $\mathrm{C}{\mathrm{H}}_4$ has a total of 6 degrees of freedom. Choose the correct answer from the options given below :

1. A.(B) and (C) only
2. B.(B) and (D) only
3. C.(A) and (B) only
4. D.(C) and (D) only