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$V_{rms},V_{av},V_{mp}$ are root mean square, average and most probable speeds of molecules of a gas obeying Maxwellian velocity distribution. Which of the following statements is correct?
1. $V_{rms}<V_{av}<V_{mp}$
2. $V_{rms}>V_{av}>V_{mp}$
3. $V_{rms}<mspace\; width="1em"></mspace><<mspace\; width="1em"></mspace>V_{av}>V_{mp}$
4. $V_{avg}>V_{rms}<V_{mp}$

Gas is found to obey the law $P^{2}V$ = constant. The initial temperature and volume are $T_0$ and $V_0$. If the gas expands to a volume $3V_0$, its final temperature becomes:
1. $\frac{T_0}{3}$           
2. $\frac{T_0}{\sqrt{3}}$
3. $3T_0$           
4. None of these

For a gas, the r.m.s speed at 800 K is:
1. Four times the value at 200 K
2. Half the value at 200 K
3. Twice the value at 200 K
4. Same as at 200 K

The mean translational kinetic energy of a perfect gas molecule at the temperature T Kelvin is:
1. $\frac{1}{2}kT$         
2. kT             
3. $\frac{3}{2}kT$           
4. 2 kT

The curve between absolute temperature and \({v}^2_{rms}\)${\mathrm{}}^{}$ is:

1.		2.
3.		4.

At constant temperature, on increasing the pressure of a gas by 5% , its volume will decrease by:          
1. 5%       
2. 5.26 %         
3. 4.26 %         
4. 4.76 %

One liter of gas A and two liters of gas B, both having the same temperature 100$°$C and the same pressure 2.5 bar will have the ratio of average kinetic energies of their molecules as:
1. 1:1       
2. 1:2     
3. 1:4       
4. 4:1

Four molecules have speeds 2 km/sec, 3 km/sec, 4 km/sec and 5 km/sec.  The root mean square speed of these molecules (km/sec) is:
1. $\sqrt{\frac{54}{4}}$       
2. $\sqrt{\frac{54}{2}}$         
3. 3.5           
4. 3$\sqrt{3}$

How many degrees of freedom the gas molecules have if, under \(\text{STP}\), the gas density \(\rho = 1.3~\text{kg/m}^3\) and the velocity of sound propagation in it is \(330~\text{ms}^{-1}\)${\mathrm{}}^{}$?
1. \(3\)       
2. \(5\)         
3. \(7\)             
4. \(8\)

For gas, if the ratio of specific heats at constant pressure p and constant volume V is ${\rm Y}$, then value of degree of freedom is:
1. $\frac{\gamma +1}{\gamma -1}$           
2. $\frac{\gamma -1}{\gamma +1}$           
3. $\frac{\gamma -1}{2}$           
4. $\frac{2}{\gamma -1}$

Gases exert pressure on the walls of containing vessel because  the gas molecules:
1. Possess momentum
2. collide with each other
3. have finite volume
4. obey gas laws

What is the mass of 2 liters of nitrogen at 22.4 atmospheric pressure and 273 K?
1. 28 g               
2. 14$\times 22.4$ g
3. 56 g               
4. None of these

The root mean square speed of oxygen molecules (O2) at a certain absolute temperature is v. If the temperature is doubled and oxygen gas dissociates into oxygen atom, the rms speed would be :
1.  $\mathrm{v}<mspace\; width="1em"></mspace><mspace\; width="1em"></mspace>$
2.  $\sqrt{2}\mathrm{v}<mspace\; width="1em"></mspace><mspace\; width="1em"></mspace>$
3.  $2\mathrm{v}<mspace\; width="1em"></mspace><mspace\; width="1em"></mspace>$
4.  $2\sqrt{2}\mathrm{v}$

A gas mixture consists of 2 moles of oxygen and 4 moles of argon at temperature T. Neglecting all vibrational modes, the total internal energy of the system is
1.  4RT
2.  15RT
3.  9RT
4.  11RT

Maxwell's velocity distribution curve is given for two different temperatures. For the given curves-
                    
1. $T_1>T_2$
2. $T_1<T_2$
3. $T_1\le T_2$
4. $T_1=T_2$

The molecules of a given mass of gas have rms velocity of 200 ms^-1 at \(27^{\circ}\mathrm{C}\) and 1.0 x 10⁵ Nm^-2 pressure. When the temperature and pressure of the gas are increased to, respectively, \(127^{\circ}\mathrm{C}\) and 0.05 X 10⁵ Nm^-2, rms velocity of its molecules in ms^-1 will become:
1. 400/√3
2. 100√2/3
3. 100/3 
4.100√2

Under which of the following conditions is the law PV = RT obeyed most closely by a real gas
1. High pressure and high temperature
2. Low pressure and low temperature
3. Low pressure and high temperature
4. High pressure and low temperature

That gas cannot be liquified :
1. Which obeys Vander Waal's equation
2. Which obeys gas equation at every temperature and pressure
3. The molecules of which are having potential energy
4. Which is a inert gas

A balloon contains $500<mspace\; width="1em"></mspace>{\mathrm{m}}^3$ of helium at 27°C and 1 atmosphere pressure. The volume of the helium at – 3°C temperature and 0.5 atmosphere pressure will be :
1.  $500<mspace\; width="1em"></mspace>{\mathrm{m}}^3$                                 
2.  $700<mspace\; width="1em"></mspace>{\mathrm{m}}^3$
3.  $900<mspace\; width="1em"></mspace>{\mathrm{m}}^3$                                 
4. $1000<mspace\; width="1em"></mspace>{\mathrm{m}}^3$

A given mass of a gas is allowed to expand freely until its volume becomes double. If ${\mathrm{C}}_{\mathrm{b}}$ and ${\mathrm{C}}_{\mathrm{a}}$ are the velocities of sound in this gas before and after expansion respectively, then ${\mathrm{C}}_{\mathrm{a}}$ is equal to :
1. $2{\mathrm{C}}_{\mathrm{b}}$                                 
2. $\sqrt{2}{\mathrm{C}}_{\mathrm{b}}$
3. ${\mathrm{C}}_{\mathrm{b}}$                                   
4. $\frac{1}{\sqrt{2}}{\mathrm{C}}_{\mathrm{b}}$

The molecular weight of a gas is 44. The volume occupied by 2.2 g of this gas at $0°\mathrm{C}$ and 2 atm pressure will be-
1.  0.56 litre                           
2.  1.2 litres
3.  2.4 litres                           
4.  5.6 litres

In the relation $\mathrm{n}=\frac{\mathrm{PV}}{\mathrm{RT}},<mspace\; width="1em"></mspace>\mathrm{n}=$
1.  Number of molecules                             
2.  Atomic number
3.  Mass number                                         
4.  Number of moles

The equation of state corresponding to 8 g of ${\mathrm{O}}_2$ is :
1.  PV = 8RT                           
2.  PV = RT/4
3.  PV = RT                             
4.  PV = RT/2

Three containers of the same volume contain three different gases. The masses of the molecules are ${\mathrm{m}}_1,<mspace\; width="1em"></mspace>{\mathrm{m}}_2$ and ${\mathrm{m}}_3$ and the number of molecules in their respective containers are ${\mathrm{N}}_1,<mspace\; width="1em"></mspace>{\mathrm{N}}_2$ and ${\mathrm{N}}_3$ . The gas pressure in the containers are ${\mathrm{P}}_1,<mspace\; width="1em"></mspace>{\mathrm{P}}_2$ and ${\mathrm{P}}_3$ respectively. All the gases are now mixed and put in one of the containers. The pressure P of the mixture will be :
1. $\mathrm{P}<\left({\mathrm{P}}_1+{\mathrm{P}}_2+{\mathrm{P}}_3\right)$                               
2. $\mathrm{P}=\frac{{\mathrm{P}}_1+{\mathrm{P}}_2+{\mathrm{P}}_3}{3}$
3. $\mathrm{P}={\mathrm{P}}_1+{\mathrm{P}}_2+{\mathrm{P}}_3$                                 
4. $\mathrm{P}>\left({\mathrm{P}}_1+{\mathrm{P}}_2+{\mathrm{P}}_3\right)$

Two thermally insulated vessels 1 and 2 are filled with air at temperatures $\left({\mathrm{T}}_1,<mspace\; width="1em"></mspace>{\mathrm{T}}_2\right),$ volume $\left({\mathrm{V}}_1,<mspace\; width="1em"></mspace>{\mathrm{V}}_2\right)$ and pressure $\left({\mathrm{P}}_1,<mspace\; width="1em"></mspace>{\mathrm{P}}_2\right)$ respectively. If the valve joining the two vessels is opened, the temperature inside the vessel at equilibrium will be
1. ${\mathrm{T}}_1+{\mathrm{T}}_2$                               
2. $\left({\mathrm{T}}_1+{\mathrm{T}}_2\right)/2$
3. $\frac{{\mathrm{T}}_1{\mathrm{T}}_2\left({\mathrm{P}}_1{\mathrm{V}}_1+{\mathrm{P}}_2{\mathrm{V}}_2\right)}{{\mathrm{P}}_1{\mathrm{V}}_1{\mathrm{T}}_2+{\mathrm{P}}_2{\mathrm{V}}_2{\mathrm{T}}_1}$                 
4. $\frac{{\mathrm{T}}_1{\mathrm{T}}_2\left({\mathrm{P}}_1{\mathrm{V}}_1+{\mathrm{P}}_2{\mathrm{V}}_2\right)}{{\mathrm{P}}_1{\mathrm{V}}_1{\mathrm{T}}_2+{\mathrm{P}}_2{\mathrm{V}}_2{\mathrm{T}}_2}$

The value of critical temperature in terms of Vander Waal’s constant a and b is
1. ${\mathrm{T}}_{\mathrm{c}}=\frac{8<mspace\; width="1em"></mspace>\mathrm{a}}{27<mspace\; width="1em"></mspace>\mathrm{Rb}}$                           
2. ${\mathrm{T}}_{\mathrm{c}}=\frac{\mathrm{a}}{2<mspace\; width="1em"></mspace>\mathrm{Rb}}$
3. ${\mathrm{T}}_{\mathrm{c}}=\frac{8}{27<mspace\; width="1em"></mspace>\mathrm{Rb}}$                             
4. ${\mathrm{T}}_{\mathrm{c}}=\frac{27<mspace\; width="1em"></mspace>\mathrm{a}}{8<mspace\; width="1em"></mspace>\mathrm{Rb}}$

At 0°C the density of a fixed mass of a gas divided by pressure is x. At 100°C, the ratio will be:
1. $\mathrm{x}$                                   
2. $\frac{273}{373}\mathrm{x}$
3. $\frac{373}{273}\mathrm{x}$                           
4. $\frac{100}{273}\mathrm{x}$

A tyre kept outside in sunlight bursts off after sometime because of :
1. Increase in pressure                                 
2. Increases in volume
3. Both (a) and (b)                                       
4. None of these

The respective speeds of the molecules are 1, 2, 3, 4 and 5 km/sec. The ratio of their r.m.s. velocity and the average velocity will be
1. $\sqrt{11}<mspace\; width="1em"></mspace>\mathbf{:}<mspace\; width="1em"></mspace>3$                                   
2. $3\mathbf{\hspace{0.17em}}\mathbf{:}<mspace\; width="1em"></mspace>\sqrt{11}$
3. $1<mspace\; width="1em"></mspace>\mathbf{:}<mspace\; width="1em"></mspace>2$                                         
4. $3<mspace\; width="1em"></mspace>\mathbf{:}<mspace\; width="1em"></mspace>4$

At a given temperature the root mean square velocities of oxygen and hydrogen molecules are in the ratio
1.  16 : 1                               
2.  1 : 16
3.  4 : 1                                 
4.  1 : 4

At a given temperature if ${\mathrm{V}}_{\mathrm{rms}}$ is the root mean square velocity of the molecules of a gas and ${\mathrm{V}}_{\mathrm{s}}$ the velocity of sound in it, then these are related as $\left(\mathrm{\gamma }=\frac{{\mathrm{C}}_{\mathrm{P}}}{{\mathrm{C}}_{\mathrm{v}}}\right)$
1. ${\mathrm{V}}_{\mathrm{rms}}={\mathrm{V}}_{\mathrm{s}}$                             
2. ${\mathrm{V}}_{\mathrm{rms}}=\sqrt{\frac{3}{\mathrm{\gamma }}}\times {\mathrm{V}}_{\mathrm{s}}$
3. ${\mathrm{V}}_{\mathrm{rms}}=\sqrt{\frac{\mathrm{\gamma }}{3}}\times {\mathrm{V}}_{\mathrm{s}}$                   
4. ${\mathrm{V}}_{\mathrm{rms}}=\left(\frac{3}{\mathrm{\gamma }}\right)\times {\mathrm{V}}_{\mathrm{s}}$

Two different isotherms representing the relationship between pressure P and volume V at a given temperature of the same ideal gas are shown for masses ${\mathrm{m}}_1$ and ${\mathrm{m}}_2$ of the gas respectively in the figure given, then

1. ${\mathrm{m}}_1<mspace\; width="1em"></mspace>><mspace\; width="1em"></mspace>{\mathrm{m}}_2$                             
2. ${\mathrm{m}}_1<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>{\mathrm{m}}_2$
3. ${\mathrm{m}}_1<mspace\; width="1em"></mspace><<mspace\; width="1em"></mspace>{\mathrm{m}}_2$                             
4. None of these

Two different masses m and 3m of an ideal gas are heated separately in a vessel of constant volume, the pressure P and absolute temperature T, graphs for these two cases are shown in the figure as A and B. The ratio of slopes of curves B to A is
 
1.  3 : 1                           
2.  1 : 3
3.  9 : 1                           
4.  1 : 9

Under constant temperature, graph between $\mathrm{P}$ and $1/\mathrm{V}$ is
1. Parabola                   
2. Hyperbola
3. Straight line             
4. Circle

If the volume of a gas at constant pressure  changes from V to 2V ,then the change in internal energy is -
1. $\frac{\mathrm{R}}{(\mathrm{\gamma }-1)}$
2. PV
3. $\frac{\mathrm{PV}}{(\mathrm{\gamma }-1)}$
$$
4. $\frac{\mathrm{\gamma PV}}{(\mathrm{\gamma }-1)}$

The degrees of freedom of a molecule of a triatomic gas are
1. 2
2. 4
3. 6
4. 8

A gas is formed of molecules each  possessing f degrees of freedom, then the value of $\mathrm{\gamma }=\frac{{\mathrm{C}}_{\mathrm{P}}}{{\mathrm{C}}_{\mathrm{V}}}$ is equal to
1. $\frac{2}{\mathrm{f}}$
2. $1+\frac{2}{\mathrm{f}}$
3. $1+\frac{\mathrm{f}}{2}$
4. $\mathrm{f}+\frac{1}{2}$

The gases carbon monoxide (CO) and nitrogen at the same temperature have kinetic energies ${\mathrm{E}}_1<mspace\; width="1em"></mspace>\mathrm{and}<mspace\; width="1em"></mspace>{\mathrm{E}}_2$ respectively. Then
1. ${\mathrm{E}}_1={\mathrm{E}}_2$
2. ${\mathrm{E}}_1>{\mathrm{E}}_2$
3. ${\mathrm{E}}_1<{\mathrm{E}}_2$
4. ${\mathrm{E}}_1<mspace\; width="1em"></mspace>\mathrm{and}<mspace\; width="1em"></mspace>{\mathrm{E}}_2$ cannot be compared

The amount of heat energy required to raise the temperature of 1g of Helium at NTP, from ${\mathrm{T}}_1\mathrm{K}<mspace\; width="1em"></mspace>\mathrm{to}<mspace\; width="1em"></mspace>{\mathrm{T}}_2\mathrm{K}$ is
1. $\frac{3}{8}{N}_A{k}_B(T_2-T_1)$
2. $\frac{3}{2}{N}_A{k}_B(T_2-T_1)$
3. $\frac{3}{4}{N}_A{k}_B(T_2-T_1)$
4. $\frac{3}{4}{N}_A{k}_B\left(\frac{T_2}{T_1}\right)$

The mean free path of molecules of a gas (radius 'r') is inversely proportional to
1. ${\mathrm{r}}^3$
2. ${\mathrm{r}}^2$
3. r
4. $\sqrt{\mathrm{r}}$

The ratio of the specific heat $\frac{{\mathrm{C}}_{\mathrm{P}}}{{\mathrm{C}}_{\mathrm{V}}}=\gamma$ in terms of degrees of freedom (n) is given by
1. $\left(1+\frac{\mathrm{n}}{3}\right)$
2. $\left(1+\frac{2}{\mathrm{n}}\right)$
3. $\left(1+\frac{\mathrm{n}}{2}\right)$
4. $\left(1+\frac{1}{\mathrm{n}}\right)$

4.0 g of gas occupies 22.4 L at STP. The specific heat capacity of the gas at constant volume is 5.0 J ${\mathrm{K}}^{-1}<mspace\; width="1em"></mspace>{\mathrm{mol}}^{-1}$. If the speed of sound in this gas at NTP is $953<mspace\; width="1em"></mspace>{\mathrm{ms}}^{-1}$, then the heat capacity at constant pressure is (Take gas constant R=8.3 $\mathrm{J}<mspace\; width="1em"></mspace>{\mathrm{K}}^{-1}<mspace\; width="1em"></mspace>{\mathrm{mol}}^{-1}$).
1. $8.5<mspace\; width="1em"></mspace>\mathrm{J}<mspace\; width="1em"></mspace>{\mathrm{K}}^{-1}<mspace\; width="1em"></mspace>{\mathrm{mol}}^{-1}$
2. $8.0<mspace\; width="1em"></mspace>\mathrm{J}<mspace\; width="1em"></mspace>{\mathrm{K}}^{-1}<mspace\; width="1em"></mspace>{\mathrm{mol}}^{-1}$
3. $7.5<mspace\; width="1em"></mspace>\mathrm{J}<mspace\; width="1em"></mspace>{\mathrm{K}}^{-1}<mspace\; width="1em"></mspace>{\mathrm{mol}}^{-1}$
4. $7.0<mspace\; width="1em"></mspace>\mathrm{J}<mspace\; width="1em"></mspace>{\mathrm{K}}^{-1}<mspace\; width="1em"></mspace>{\mathrm{mol}}^{-1}$

A given sample of an ideal gas occupies a volume V at a pressure P and absolute temperature T. The mass of each molecule of the gas is m. Which of the following gives the density of the gas?
1. Pm/(kT)
2. P/(kTV)
3. mkT
4. P/(kT)

One mole of an ideal monatomic gas undergoes a process described by the equation ${\mathrm{PV}}^3$=constant. The heat capacity of the gas during this process is
1. $\frac{5}{2}$R
2. 2R
3. R
4. $\frac{3}{2}$R

At what temperature will the rms speed of oxygen molecules become just sufficient for escaping from the Earth's atmosphere?
(Given: Mass of oxygen molecule (m)=$2.76\times {10}^{-26}$ kg, Boltzmann's constant $k_B=1.38\times {10}^{-23}<mspace\; width="1em"></mspace>J<mspace\; width="1em"></mspace>K^{-1}$)
1. $5.016\times {10}^4<mspace\; width="1em"></mspace>K$
2. $8.360\times {10}^4<mspace\; width="1em"></mspace>K$
3. $2.508\times {10}^4\mathrm{K}$
4. $1.254\times {10}^4<mspace\; width="1em"></mspace>\mathrm{K}$