JEE Main & Advanced Physics Kinetic Theory of Gases Question Bank

Self Evaluation Test - Kinetic Theory Total Questions - 100

1)

The velocity of sound in air is \[332\text{ }m\text{ }{{s}^{-1}}\] at NTP. Find the rms speed of air molecules at NTP. \[\left( \gamma =1.41 \right)\]

A)
\[484\text{ }m{{s}^{-1}}\]

B)
\[418\text{ }m{{s}^{-1}}\]

C)
\[248\text{ }m{{s}^{-1}}\]

D)
\[382\text{ }m{{s}^{-1}}\]
View Solution
2)

The density of a gas is \[6\times {{10}^{-2}}kg/{{m}^{3}}\] and the root mean square velocity of the gas molecules is 500 m/s. The pressure exerted by the gas on the walls of the vessel is

A)
\[5\times {{10}^{3}}N/{{m}^{2}}\]

B)
\[1.1\times {{10}^{-4}}N/{{m}^{2}}\]

C)
\[0.83\times {{10}^{-4}}N/{{m}^{2}}~\]

D)
\[30N/{{m}^{2}}\]
View Solution
3)

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 (in km/sec) is

A)
\[\sqrt{54/4}\]

B)
\[\sqrt{54/2}\]

C)
3.5

D)
\[3\sqrt{3}\]
View Solution
4)

The absolute gas temperature at which the root mean square speed of helium molecules exceeds their most probable speed by 200 m/s is

A)
110.2 K

B)
90.2 K

C)
190.2 K

D)
100.2 K
View Solution
5)

N (< 100) molecules of a gas have velocities 1, 2, 3,........ N km/s respectively. Then ratio of rms speed and average speed is

A)
1

B)
\[\frac{\sqrt{\left( 2N+1 \right)\left( N+1 \right)}}{6N}\]

C)
\[\frac{\sqrt{\left( 2N+1 \right)\left( N+1 \right)}}{6}\]

D)
\[2\sqrt{\frac{2N+1}{6\left( N+1 \right)}}\]
View Solution
6)

If the molecules in a tank of hydrogen have the same RMS speed as the molecules in another tank of oxygen, we may be sure that

A)
the pressures are the same

B)
the hydrogen is at the higher temperature

C)
the temperatures are the same

D)
the oxygen is at the higher temperature
View Solution
7)

\[{{H}_{2}},\,~{{O}_{2}},\text{ }{{N}_{2}}\] and \[He\] are enclosed in identical containers under the similar conditions of pressure and temperature. The gases will have

A)
same R.M.S. speed

B)
same \[\frac{K.E}{kg}\]

C)
different \[\frac{K.E.}{mole}\]

D)
same \[\frac{K.E.}{vol}\]
View Solution
8)

When do real gases approach the ideal gas behaviour?

A)
At low pressure and low temperature

B)
At low pressure and high temperature

C)
At high pressure and high temperature

D)
At high pressure and low temperature
View Solution
9)

According to the kinetic theory of gases, the pressure exerted by a gas on the wall of the container is measured as

A)
rate of change of momentum imparted to the walls per second per unit area.

B)
momentum imparted to the walls per unit area

C)
change of momentum imparted to the walls per unit volume.

D)
change in momentum per unit volume
View Solution
10)

In kinetic theory of gases, which of the following statement regarding elastic collisions of the molecules is wrong?

A)
Kinetic energy is lost in collisions

B)
Kinetic energy remains constant in collision

C)
Momentum is conserved in collision

D)
Pressure of the gas remains constant in collisions
View Solution
11)

At room temperature a diatomic gas is found to have an r. m. s. speed of \[1930\text{ }m{{s}^{-1}}\]. The gas is:

A)
\[{{H}_{2}}\]

B)
\[C{{l}_{2}}\]

C)
\[{{O}_{2}}\]

D)
\[{{F}_{2}}\]
View Solution
12)

Gases exert pressure on the walls of containing vessel because the gas molecules

A)
possess momentum

B)
collide with each other

C)
have finite volume

D)
obey gas laws
View Solution
13)

Consider a gas with density \[\rho \] and \[\overline{c}\] as the root mean square velocity of its molecules contained in a volume. If the system moves as whole with velocity, then the pressure exerted by the gas is

A)
\[\frac{1}{3}\rho {{\bar{c}}^{2}}\]

B)
\[\frac{1}{3}\rho {{\left( c+\nu \right)}^{2}}\]

C)
\[\frac{1}{3}\rho {{\left( \bar{c}-\nu \right)}^{2}}\]

D)
       \[\frac{1}{3}\rho {{\left( {{{\bar{c}}}^{2}}-\nu \right)}^{2}}\]
View Solution
14)

The pressure of a gas is raised from \[27{}^\circ C\]to \[927{}^\circ C.\]The root mean square speed is

A)
\[\sqrt{\left( 927/27 \right)}\] times the earlier value

B)
remain the same

C)
gets halved

D)
get doubled
View Solution
15)

Why does the pressure of an ideal gas increase when it is heated at constant volume?

A)
The gas molecules expand

B)
The molecules move at the same speed, but

C)
The molecules move faster and hit the walls more often

D)
The number of molecules of gas increases
View Solution
16)

Maxwell's velocity distribution curve is given for two different temperature. For the given curves.

A)
\[{{T}_{1}}>{{T}_{2}}\]

B)
\[{{T}_{1}}<{{T}_{2}}\]

C)
\[{{T}_{1}}\le {{T}_{2}}\]

D)
\[{{T}_{1}}={{T}_{2}}\]
View Solution
17)

Helium gas is filled in a closed vessel (having negligible thermal expansion coefficient) when it is heated from 300 K to 600 K, then average kinetic energy of helium atom will be

A)
\[\sqrt{2}\] times

B)
2 times

C)
unchanged

D)
half
View Solution
18)

The temperature of an ideal gas is increased from 120 K to 480 K. If at 120 K the root-mean-square velocity of the gas molecules is v, at 480 K it becomes

A)
4v

B)
2v

C)
v/2

D)
v/4
View Solution
19)

Figure shows a parabolic graph between T and 1/V for a mixture of a gas undergoing an adiabatic process. What is the ratio of \[{{V}_{rms}}\] of molecules and speed of sound in mixture?

A)
\[\sqrt{3/2}\]

B)
\[\sqrt{2}\]

C)
\[\sqrt{2/3}\]

D)
\[\sqrt{3}\]
View Solution
20)

A nitrogen molecule has some rms speed at \[0{}^\circ C\]on the surface of the earth. With this speed, it goes straight up. If there is no collisions with other molecules, the molecule will rise up to a height of

A)
82 km

B)
12.4 km

C)
10.6 km

D)
152 km
View Solution
21)

At constant volume, temperature is increased then

A)
collision on walls will be less

B)
number of collisions per unit time will increase

C)
collisions will be in straight lines

D)
collisions will not change
View Solution
22)

At what temperature is the r. m. s velocity of a hydrogen molecule equal to that of an oxygen molecule at \[47{}^\circ C\]?

A)
80 K

B)
-73 K

C)
3 K

D)
20 K
View Solution
23)

Modern vacuum pumps can evacuate a vessel down to a pressure of \[4.0\times {{10}^{-15}}\text{ }atm.\]at room temperature (300 K). Taking , \[1\text{ }atm=105\text{ }Pa\]and \[{{N}_{avogadro}}=6\times {{10}^{23}}mol{{e}^{-1}},\] the mean distance between molecules of gas in an evacuated vessel will be of the order of:

A)
0.2 urn

B)
0.2 mm

C)
0.2 cm

D)
0.2 nm
View Solution
24)

The quantity of gas in a closed vessel is halved and the velocities of its molecules are doubled. The final pressure of the gas will be

A)
P

B)
2P

C)
P/2

D)
4P
View Solution
25)

Pressure versus temperature graph of an ideal gas of equal number of moles of different volumes are plotted as shown in figure. Choose the correct alternative

A)
\[{{V}_{1}}={{V}_{2}};{{V}_{3}}={{V}_{4}}\text{ and }{{V}_{2}}>{{V}_{3}}\]

B)
\[{{V}_{1}}={{V}_{2}};{{V}_{3}}={{V}_{4}}\text{ and }{{V}_{2}}<{{V}_{3}}\]

C)
\[{{V}_{1}}={{V}_{2}}={{V}_{3}}={{V}_{4}}\]

D)
\[{{V}_{4}}>{{V}_{3}}>{{V}_{2}}>{{V}_{1}}\]
View Solution
26)

Consider a collection of a large number of dust particles each with speed v. The direction of velocity is randomly distributed in the collection. What is the magnitude of the relative velocity between a pairs in the collection?

A)
\[\frac{3v}{\pi }\]

B)
\[\frac{4v}{\pi }\]

C)
\[\frac{2v}{\pi }\]

D)
\[\frac{v}{\pi }\]
View Solution
27)

Relation between pressure (P) and energy (E) of gas is

A)
\[P=\frac{2}{3}E\]

B)
\[P=\frac{1}{3}E\]

C)
\[P=\frac{1}{2}E\]

D)
\[P=3E\]
View Solution
28)

Five gas molecules chosen at random are found to have speeds of 500, 600, 700, 800 and 900 m/s

A)
the root mean square speed and the average

B)
the root mean square speed is 14 m/s higher than the average speed.

C)
the root mean square speed is 14 m/s lower than the average speed.

D)
the root mean square speed is \[\sqrt{14}\text{ m/s}\]higher than the average speed.
View Solution
29)

Two containers A and B are partly filled with water and closed. The volume of A is twice that of B and it contains half the amount of water in B. If both are at the same temperature, the water vapor in the containers will have pressure in the ratio of

A)
1 : 2

B)
1 : 1

C)
2 : 1

D)
4 : 1
View Solution
30)

A gas mixture consists of molecules of type 1, 2 and 3, with molar masses \[{{m}_{1}}>{{m}_{2}}>{{m}_{3}}.{{v}_{rms}}\] and \[\bar{K}\] are the r. m. s. speed and average kinetic energy of the gases. Which of the following is true?

A)
\[{{({{v}_{rms}})}_{1}}<{{({{v}_{rms}})}_{2}}<{{({{v}_{rms}})}_{3}}\] and \[{{(\bar{K})}_{1}}={{(\bar{K})}_{2}}={{(\bar{K})}_{3}}\]

B)
\[{{({{v}_{rms}})}_{1}}={{({{v}_{rms}})}_{2}}={{({{v}_{rms}})}_{3}}\]and \[{{(\bar{K})}_{1}}={{(\bar{K})}_{2}}>{{(\bar{K})}_{3}}\]

C)
\[{{({{v}_{rms}})}_{1}}>{{({{v}_{rms}})}_{2}}>{{({{v}_{rms}})}_{3}}\] and \[{{(\bar{K})}_{1}}<{{(\bar{K})}_{2}}>{{(\bar{K})}_{3}}\]

D)
\[{{({{v}_{rms}})}_{1}}>{{({{v}_{rms}})}_{2}}>{{({{v}_{rms}})}_{3}}\]and \[{{(\bar{K})}_{1}}<{{(\bar{K})}_{2}}<{{(\bar{K})}_{3}}\]
View Solution
31)

One gram mole of nitrogen at \[27{}^\circ C\]and 1 aim pressure is contained in a vessel and the molecules are moving with their rms speed. The number of collisions per second which the vessel's wall is

A)
\[2\times {{10}^{27}}\]

B)
\[~2\times {{10}^{20}}\]

C)
\[2\times {{10}^{10}}\]

D)
\[~2\times {{10}^{24}}\]
View Solution
32)

In an ideal gas at temperature T, the average force that a molecule applies on the walls of a closed container depends on T as\[{{\text{T}}^{\text{q}}}\]. A good estimate for q is:

A)
\[\frac{1}{2}\]

B)
2

C)
1

D)
\[\frac{1}{4}\]
View Solution
33)

Three closed vessels A, B and C are at the same temperature T and contain gases which obey the Maxwellian distribution of velocities. Vessel A contain only\[{{O}_{2}}\], B only \[{{N}_{2}}\] and C a mixture of equal quantities of \[{{O}_{2}}\] and \[{{N}_{2}}\]. If the average speed of the \[{{O}_{2}}\] molecules in vessel A is that of the \[{{N}_{2}}\] molecules in vessel B is \[{{v}_{2}},\] the average speed of the \[{{O}_{2}}\] molecules in vessel C is

A)
\[\frac{{{v}_{1}}+{{v}_{2}}}{2}\]

B)
       \[{{v}_{1}}\]

C)
\[{{\left( {{v}_{1}}.{{v}_{2}} \right)}^{\frac{1}{2}}}\]

D)
       \[\sqrt{\frac{3kT}{M}}\]
View Solution
34)

The molecules of a given mass of a gas have r.m.s. velocity of \[200\text{ }m{{s}^{-1}}\]at \[27{}^\circ C\] and \[1.0\times {{10}^{5}}\text{ }N{{m}^{-2}}\] pressure. When the temperature and pressure of the gas are respectively, \[127{}^\circ C\]and \[0.05\times {{10}^{5}}\text{ }N{{m}^{-2}},\]the r.m.s. velocity of its molecules

A)
\[100\sqrt{2}\]

B)
       \[\frac{400}{\sqrt{3}}\]

C)
\[\frac{100\sqrt{2}}{3}\]

D)
       \[\frac{100}{3}\]
View Solution
35)

N molecules each of mass m of a gas A and 2N molecules each of mass 2m of gas B are contained in the same vessel which is maintained at temperature T. The mean square velocity of molecules of B type is \[{{v}^{2}}\] and the mean square rectangular component of the velocity of A type is denoted by \[{{\omega }^{2}}.\] Then \[6.21\text{ }\times \text{ }{{10}^{-21}}\text{ }J\]is

A)
2

B)
1

C)
1/3

D)
2/3
View Solution
36)

The density (p)versus pressure (P) of a given mass of an ideal gas is shown at two temperatures\[~{{T}_{1}}\] and \[~{{T}_{2}}\] Then relation between \[~{{T}_{1}}\] and \[~{{T}_{2}}\] may be

A)
\[{{T}_{1}}>{{T}_{2}}\]

B)
       \[{{T}_{2}}>{{T}_{1}}\]

C)
\[{{T}_{1}}={{T}_{2}}\]

D)
       All the three are possible
View Solution
37)

Boyle' law is applicable for an

A)
adiabatic process.

B)
isothermal process.

C)
isobaric process.

D)
isochoric process
View Solution
38)

What will be the ratio of number of molecules of a monoatomic and a diatomic gas in a vessel, if the ratio of their partial pressures is 5 : 3?

A)
5 : 1

B)
       3 : 1

C)
5 : 3

D)
       3 : 5
View Solution
39)

A balloon contains \[1500\text{ }{{m}^{3}}\] of helium at \[27{}^\circ C\]and 4 atmospheric pressure. The volume of helium at \[-3{}^\circ C\] temperature and 2 atmospheric pressure will,

A)
\[1500{{m}^{3}}~\]

B)
\[~1700{{m}^{3}}\]

C)
\[1900{{m}^{3}}\]

D)
       \[~2700{{m}^{3}}\]
View Solution
40)

The figure shows graph of pressure and volume of a gas at two different temperatures \[{{T}_{1}}\]and\[{{T}_{2}}\]. Which of the following inferences is correct?

A)
\[{{T}_{1}}>{{T}_{2}}\]

B)
\[{{T}_{1}}={{T}_{2}}\]

C)
\[{{T}_{1}}<{{T}_{2}}\]

D)
None of these
View Solution
41)

The average translational kinetic energy of \[{{O}_{2}}\](relative molar mass 32) molecules at a particular temperature is 0.048 eV. The translational kinetic energy of \[{{N}_{2}}\] (relative molar mass 28) molecules in eV at the same temperature is

A)
0.0015

B)
0.003

C)
0.048

D)
0.768
View Solution
42)

At \[10{}^\circ C\] the value of the density of a fixed mass of an ideal gas divided by its pressure is x. At \[110{}^\circ C\]this ratio is:

A)
x

B)
\[\frac{383}{283}x\]

C)
\[\frac{10}{110}x\]

D)
\[\frac{283}{383}x\]
View Solution
43)

Two vessels separately contain two ideal gases A and B at the same temperature. The pressure of A being twice that of B. Under such conditions, the density of A is found to be 1.5 times the density of B. The ratio of molecular weight of A and B is:

A)
\[\frac{3}{4}\]

B)
\[2~\]

C)
\[\frac{1}{2}\]

D)
\[\frac{2}{3}\]
View Solution
44)

A perfect gas at \[27{}^\circ C\] is heated at constant pressure so as to double its volume. The final temperature of the gas will be, close to

A)
(a)\[327{}^\circ C\]

B)
       \[200{}^\circ C\]

C)
\[54{}^\circ C\]

D)
       \[300{}^\circ C\]
View Solution
45)

The average translational energy and the rms speed of molecules in a sample of oxygen gas at 300 K are \[6.21\text{ }\times \text{ }{{10}^{-21}}\text{ }J\] and 484 m/s respectively The corresponding values at 600 K are nearly (assuming ideal gas behavior)

A)
\[12.42\times {{10}^{-21}}J,928m/s\]

B)
\[8.78\times {{10}^{-21}}J,684m/s\]

C)
\[6.21\times {{10}^{-21}}J,968m/s\]

D)
\[12.42\times {{10}^{-21}}J,684m/s\]
View Solution
46)

The temperature of an air bubble while rising from bottom to surface of a lake remains constant but its diameter is doubled if the pressure on the surface is equal to h meter of mercury column and relative density of mercury is \[\rho \] then the depth of lake in meter is

A)
\[2\rho h\]

B)
\[4\rho h\]

C)
\[8\rho h\]

D)
\[7\rho h\]
View Solution
47)

Three containers of the same volume contain three different gases. The masses of the molecules are \[{{m}_{1}},{{m}_{2}}\]and \[{{m}_{3}}\]the number of\[{{N}_{1}}\], \[{{N}_{2}}\] and \[{{N}_{3}}.\] The gas pressure in the containers \[{{P}_{1}},{{P}_{2}}\] and \[{{P}_{3}}\] respectively. All the gases are now mixed and put in one of these containers. The pressure P of the mixture will be

A)
\[P<\left( {{P}_{1}}+{{P}_{2}}+{{P}_{3}} \right)\]

B)
\[P=\frac{{{P}_{1}}+{{P}_{2}}+{{P}_{3}}}{3}\]

C)
\[P={{P}_{1}}+{{P}_{2}}+{{P}_{3}}\]

D)
\[P>\left( {{P}_{1}}+{{P}_{2}}+{{P}_{3}} \right)\]
View Solution
48)

Temperature of a body is only on manifestation of the mean

A)
total mechanical energy of a molecule of the body

B)
potential energy of a molecule of the body

C)
rotational kinetic energy of a molecule of the body

D)
translational kinetic energy of a molecule of the body
View Solution
49)

The mean free path of molecules of a gas, (radius

A)
\[{{r}^{3}}\]

B)
\[{{r}^{2}}\]

C)
\[r\]

D)
       \[\sqrt{r}\]
View Solution
50)

A closed hollow insulated cylinder is filled with gas at \[0{}^\circ C\]and also contains an insulated piston of negligible weight and negligible thickness at the middle point. The gas on one side of the piston is heated to \[100{}^\circ C.\]If the piston moves 5 cm, the length of the hollow cylinder is

A)
13.65 cm

B)
27.3 cm

C)
38.6 cm

D)
64.6 cm
View Solution
51)

An air bubble of volume \[{{v}_{0}}\] is released by a fish at a depth h in a lake. The bubble rises to the standard atmospheric pressure above the lake. The volume of the bubble just before touching the surface will be (density of water is p)

A)
\[{{v}_{0}}\]

B)
\[{{v}_{0}}\left( \rho gh/p \right)\]

C)
\[{{N}_{2}}\]

D)
\[{{v}_{0}}\left( 1+\frac{\rho gh}{p} \right)\]
View Solution
52)

One kg of a diatomic gas is at a pressure of \[8\times {{10}^{4}}N/{{m}^{2}}.\] The density of the gas is4kg/m3. What is the energy of the gas due to its thermal motion?

A)
\[5\times {{10}^{4}}J\]

B)
\[6\times {{10}^{4}}J\]

C)
\[7\times {{10}^{4}}J\]

D)
\[3\times {{10}^{4}}J\]
View Solution
53)

The maximum attainable temperature of ideal gas in the process \[P={{P}_{0}}-\alpha {{V}^{2}}\] where \[{{P}_{0}}\]and \[\alpha \] are +ve constants.

A)
\[\frac{2{{P}_{0}}}{3nR}{{\left( \frac{{{P}_{0}}}{3\alpha } \right)}^{1/2}}\]

B)
\[\frac{{{P}_{0}}}{2nR}{{\left( \frac{2{{P}_{0}}}{3\alpha } \right)}^{1/2}}\]

C)
\[\frac{2nR}{{{P}_{0}}}{{\left( \frac{2{{P}_{0}}}{3\alpha } \right)}^{1/2}}\]

D)
\[\frac{2{{P}_{0}}}{nR}{{\left( \frac{{{P}_{0}}}{2\alpha } \right)}^{1/2}}\]
View Solution
54)

In the given (V - T) diagram, what is the relation between pressure \[{{P}_{1}}\] and\[{{P}_{2}}\]?

A)
\[{{P}_{2}}>{{P}_{1}}\]

B)
\[{{P}_{2}}<{{P}_{1}}\]

C)
Cannot be predicted

D)
\[{{P}_{2}}={{P}_{1}}\]
View Solution
55)

One mole of an ideal gas undergoes a process\[P=\frac{{{P}_{0}}}{1+{{\left( \frac{{{V}_{0}}}{V} \right)}^{2}}}\] Here \[{{P}_{0}}\] and \[{{V}_{0}}\] are constant. Change in temperature of the gas when volume is changed from \[V={{V}_{0}}\] to \[V=2{{V}_{0}}\]

A)
\[\frac{-2{{P}_{0}}{{V}_{0}}}{5R}\]

B)
\[\frac{11{{P}_{0}}{{V}_{0}}}{10R}\]

C)
\[\frac{-5{{P}_{0}}{{V}_{0}}}{10R}\]

D)
\[{{P}_{0}}{{V}_{0}}\]
View Solution
56)

The internal energy of monatomic and diatomic gases are respectively due to

A)
linear motion and rolling motion

B)
rolling motion and linear motion

C)
linear motion and rotatory motion

D)
rotatory motion and linear motion
View Solution
57)

The equation of state for 5 g of oxygen at a pressure P and temperature T, when occupying a volume V, will be where R is the gas constant.

A)
\[PV=(5/16)RT~~\]

B)
\[PV=(5/32)RT\]

C)
\[PV=5RT~\]

D)
\[PV=(5/2)RT\]
View Solution
58)

A gas at \[27{}^\circ C\] temperature and 30 atmospheric pressure is allowed to expand to the atmospheric pressure. If the volume becomes 10 times its initial volume, then the final temperature becomes

A)
\[100{}^\circ C\]

B)
\[173{}^\circ C\]

C)
\[273{}^\circ C\]

D)
\[-173{}^\circ C\]
View Solution
59)

Air is pumped into an automobile tube up to a pressure of 200 kPa in the morning when the air temperature is \[22{}^\circ C.\] During the day, temperature rises to \[42{}^\circ C\] and the tube expands by 2%. The pressure of the air in the tube at this temperature, will be approximately

A)
212 kPa

B)
209 kPa

C)
206 kPa

D)
200 kPa
View Solution
60)

Which of the following will have maximum total kinetic energy at temperature 300K?

A)
\[1kg{{H}_{2}}\]

B)
\[1kgHe\]

C)
\[\frac{1}{2}1kg{{H}_{2}}+\frac{1}{2}1kgHe\]

D)
\[\frac{1}{4}1kg{{H}_{2}}+\frac{3}{4}1kgHe\]
View Solution
61)

One liter of oxygen at a pressure of 1 atm, and 2 liters of nitrogen at a pressure of 0.5 atm. Are introduced in the vessel of 1 liter capacity, without any change in temperature. The total pressure would be

A)
1.5 atm.

B)
0.5 atm.

C)
2.0 atm.

D)
1.0 atm.
View Solution
62)

The degree of freedom of a molecule of a triatomic gas is

A)
2

B)
4

C)
6

D)
8
View Solution
63)

A polyatomic gas with n degrees of freedom has a mean energy per molecule given by

A)
\[\frac{nkT}{N}\]

B)
\[\frac{nkT}{2N}\]

C)
\[\frac{nkT}{2}\]

D)
\[\frac{3kT}{2}\]
View Solution
64)

A vessel contains a mixture of one mole of oxygen and two moles of nitrogen at 300 K. The ratio of the average rotational kinetic energy per molecule to that per N, molecule is

A)
1 : 1

B)
1 : 2

C)
2 : 1

D)
depends on the moments of inertia of the two molecules
View Solution
65)

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

A)
3 : 1

B)
1 : 3

C)
9 : 1

D)
1 : 9
View Solution
66)

Two gases occupy two containers A and B the gas in A, of volume \[0.10{{m}^{3}}\], exerts a pressure of 1.40 MPa and that in B of volume \[0.15{{m}^{3}}\] exerts a pressure 0.7 MPa. The two containers are united by a tube of negligible volume and the gases are allowed to intermingle. Then if the temperature remains constant, the final pressure in the container will be (in MPa)

A)
0.70

B)
0.98

C)
1.40

D)
210
View Solution
67)

Two thermally insulated vessels 1 and 2 are filled with air at temperatures \[\] volume \[({{V}_{1}},\text{ }{{\text{V}}_{2}})\]and pressure \[({{P}_{1}},\text{ }{{\text{P}}_{2}})\] respectively. If the valve joining the two vessels is opened, the temperature inside the vessel at equilibrium will be

A)
\[{{T}_{1}}+{{T}_{2}}\]

B)
\[({{T}_{1}}+{{T}_{2}})/2\]

C)
\[\frac{{{T}_{1}}{{T}_{2}}\left( {{P}_{1}}{{V}_{1}}+{{P}_{2}}{{V}_{2}} \right)}{{{P}_{1}}{{V}_{1}}{{T}_{2}}+{{P}_{2}}{{V}_{2}}{{T}_{1}}}\]

D)
\[\frac{{{T}_{1}}{{T}_{2}}\left( {{P}_{1}}{{V}_{1}}+{{P}_{2}}{{V}_{2}} \right)}{{{P}_{1}}{{V}_{1}}{{T}_{1}}+{{P}_{2}}{{V}_{2}}{{T}_{2}}}\]
View Solution
68)

The equation of state of a gas is given by \[\left( P+\frac{a{{T}^{2}}}{V} \right){{V}^{c}}=\left( RT+b \right)\]where a, b, c and R are constants. The isotherms can be represented \[P=A{{V}^{m}}-B{{V}^{n}},\] where A and 5 depend only on temperature and

A)
\[m=-c\text{ and }n=-1\]

B)
\[m=c\text{ and }n=-1\]

C)
\[m=-c\text{ and }n=1\]

D)
\[m=c\text{ and }n=-1\]
View Solution
69)

An ideal gas is expanding such that \[P{{T}^{2}}=\]constant. The coefficient of volume expansion of the gas is

A)
1/T

B)
2/T

C)
3/T

D)
4/T
View Solution
70)

A non-linear triatomic gas is filled inside a vessel. If 'a' fraction of moles dissociate into individual atoms, then average degree of freedom for the mixture is: (neglect vibrational degrees of freedom)

A)
\[\frac{3\alpha +6}{\alpha +1}\]

B)
\[\frac{\alpha +6}{2\alpha +1}\]

C)
\[\frac{3\alpha +6}{\alpha +2}\]

D)
\[\frac{3\alpha +6}{2\alpha +1}\]
View Solution
71)

The amount of heat energy required to raise the temperature 1g of Helium at NTP, from T,K to

A)
\[\frac{3}{2}{{N}_{a}}{{k}_{B}}\left( {{T}_{2}}-{{T}_{1}} \right)\]

B)
\[\frac{3}{4}{{N}_{a}}{{k}_{B}}\left( {{T}_{2}}-{{T}_{1}} \right)\]

C)
\[\frac{3}{4}{{N}_{a}}{{k}_{B}}\frac{{{T}_{2}}}{{{T}_{1}}}\]

D)
\[\frac{3}{8}{{N}_{a}}{{k}_{B}}\left( {{T}_{2}}-{{T}_{1}} \right)\]
View Solution
72)

The specific heat of a gas

A)
has only two values \[{{c}_{p}}\] and \[{{c}_{v}}\]

B)
has a unique value at a given temperature

C)
can have any value between 0 and \[\infty \]

D)
depends upon the mass of the gas
View Solution
73)

The specific heats at constant pressure is greater than that of the same gas at constant volume because

A)
at constant pressure work is done in expanding the gas

B)
at constant volume work is done in expanding the gas

C)
the molecular attraction increases more at constant pressure

D)
the molecular vibration increases more at constant pressure
View Solution
74)

During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio \[\frac{{{C}_{p}}}{{{C}_{v}}}=\gamma \] for the gas is

A)
2

B)
3/2

C)
5/3

D)
4/3
View Solution
75)

A mixture of \[{{n}_{1}}\] moles of monoatomic gas and \[{{n}_{2}}\] moles of diatomic gas has \[\frac{{{C}_{p}}}{{{C}_{v}}}=\gamma =1.5\]then

A)
\[{{n}_{1}}={{n}_{2}}\]

B)
\[2{{n}_{1}}={{n}_{2}}\]

C)
\[{{n}_{1}}=2{{n}_{2}}\]

D)
\[2{{n}_{1}}=3{{n}_{2}}\]
View Solution
76)

Two moles of ideal helium gas are in a rubber balloon at \[30{}^\circ C.\] The balloon is fully expandable and can be assumed to require no energy in its expansion. The temperature of the gas in the balloon is slowly changed to \[35{}^\circ C.\] The amount of heat required in raising the temperature is nearly (take R = 8.31 J/mol. K)

A)
62 J

B)
104 J

C)
124 J

D)
208 J
View Solution
77)

Two cylinders A and B fitted with pistons contain equal amounts of an ideal diatomic gas at 300 K. The piston of A is free to move, while that B is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise in temperature of the gas in A is 30 K, then the rise in temperature of the gas in B is

A)
30 K

B)
18 K

C)
50 K

D)
42 K
View Solution
78)

When an ideal diatomic gas is heated at constant pressure, the fraction of the heat energy supplied which increases the internal energy of the gas is

A)
2/5

B)
3/5

C)
3/7

D)
5/7
View Solution
79)

If one mole of a monatomic gas \[\left( \gamma =\frac{5}{3} \right)\]is mixed with one mole of a diatomic gas \[\left( \gamma =\frac{7}{5} \right)\], the value of Y for mixture is

A)
1.40

B)
1.50

C)
1.53

D)
3.07
View Solution
80)

4.0 g of a gas occupies 22.4 liters at NTP. The specific heat capacity of the gas at constant volume is \[5.0J{{K}^{-1}}.\]If the speed of sound in this gas at NTP is \[952\text{ }m{{s}^{-1}},\] then the heat capacity at constant pressure is (Take gas constant \[R=8.3\text{ }J{{K}^{-1}}mo{{l}^{-1}}\])

A)
\[7.5\text{ }J{{K}^{-1}}mo{{l}^{-1}}\]

B)
\[7.0\text{ }J{{K}^{-1}}mo{{l}^{-1}}\]

C)
\[8.5J{{K}^{-1}}mo{{l}^{-1}}\]

D)
\[8.0\text{ }J{{K}^{-1}}mo{{l}^{-1}}\]
View Solution
81)

The molar specific heats of an ideal gas at constant pressure and volume are denoted by \[{{C}_{p}}\] and\[{{C}_{v}}\], respectively. If \[\gamma =\frac{{{C}_{p}}}{{{C}_{v}}}\] and R is the universal gas constant, then Cy is equal to

A)
\[\frac{R}{\left( \gamma -1 \right)}\]

B)
\[\frac{\left( \gamma -1 \right)}{R}\]

C)
\[\gamma R\]

D)
\[\frac{1+\gamma }{1-\gamma }\]
View Solution
82)

The specific heat of \[Ar\] at constant volume is \[0.075\text{ }k{{g}^{-1}}{{K}^{-1}}.\] Calculate the atomic weight \[~\left( R=2\text{ }cal\text{ }mo{{l}^{-1}}{{K}^{-1}} \right)\]

A)
40

B)
40.4

C)
40.2

D)
40.80
View Solution
83)

A mixture of ideal gases \[{{N}_{2}}\]and He are taken in the mass ratio of 14 : 1 respectively Molar heat capacity of the mixture at constant pressure is

A)
6R/19

B)
13R/6

C)
6R/13

D)
19R/6
View Solution
84)

The ratio \[{{C}_{p}}/{{C}_{v}}\] for a gas mixture consisting of 8g of helium and 16 g of oxygen is

A)
24.2/15

B)
       15/23

C)
27/17

D)
       17/27
View Solution
85)

The molar specific heat at constant pressure of an ideal gas is (7/2) R. The ratio of specific heat at constant pressure to that at constant volume is

A)
8/7

B)
5/7

C)
9/7

D)
7/5
View Solution
86)

If for a gas, the gas is made up of molecules which are

A)
diatomic

B)
mixture of diatomic and polyatomic molecules

C)
monoatomic

D)
polyatomic
View Solution
87)

At very high temperatures vibrational degrees also becomes active. At such temperatures an ideal diatomic gas has a molar specific heat at constant pressure, \[{{C}_{p}}\] is

A)
3R/2

B)
5R/2

C)
6R/2

D)
9R/2
View Solution
88)

For hydrogen gas, \[{{C}_{p}}-{{C}_{v}}=a,\] and for oxygen gas, \[{{C}_{p}}-{{C}_{v}}=b,\] so the relation between a and b is given by

A)
\[a=16b\]

B)
\[16b=a\]

C)
\[a=4b~\]

D)
a=b
View Solution
89)

The value of \[{{C}_{p}}-{{C}_{v}}\] is 1.00R for a gas sample in state A and is 1.06R in state B. Let \[{{P}_{A}},{{P}_{B}}\] denote the pressure and \[{{T}_{A}},{{T}_{B}}\] denote the temperature of the states A and B respectively. Then most likely

A)
\[{{P}_{A}}<{{P}_{B}}\text{ and }{{T}_{A}}>{{T}_{B}}\]

B)
\[{{P}_{A}}>{{P}_{B}}\text{ and }{{T}_{A}}<{{T}_{B}}\]

C)
\[{{P}_{A}}={{P}_{B}}\text{ and }{{T}_{A}}<{{T}_{B}}\]

D)
\[{{P}_{A}}>{{P}_{B}}\text{ and }{{T}_{A}}={{T}_{B}}\]
View Solution

90)

A monoatomic ideal gas is taken through a reversible process whose equation is given by: \[p=k{{V}^{-\frac{1}{2}}}\]

Where p is the pressure and V is the volume of the gas.

The molar heat capacity of the gas in the above process, is

\[{{C}_{p}}+lR\]

\[{{C}_{v}}-lR\]

\[{{C}_{v}}+lR~\]

\[~{{C}_{p}}+2R\]

View Solution

91)

One mole of a gas occupies 22.4 lit at N.T.P. Calculate the difference between two molar specific heats of the gas. \[J=4200J/kcal.\]

A)
1.979kcal/k mol K

B)
2.378 kcal/k mol K

C)
4.569 kcal/k mol K

D)
3.028 kcal/k mol K
View Solution
92)

For a gas, difference between two specific heats is \[5000\text{ }J/mole{}^\circ C.\]If the ratio of specific heat is 1.6, the two specific heats are in \[T=190.2K.\]

A)
\[{{C}_{p}}=1.33\times {{10}^{4}},{{C}_{V}}=2.66\times {{10}^{4}}\]

B)
\[{{C}_{p}}=13.3\times {{10}^{4}},{{C}_{V}}=8.33\times {{10}^{4}}\]

C)
\[{{C}_{p}}=1.33\times {{10}^{4}},{{C}_{V}}=8.33\times {{10}^{3}}\]

D)
\[{{C}_{p}}=2.6\times {{10}^{4}},{{C}_{V}}=8.33\times {{10}^{4}}\]
View Solution
93)

The molar specific heat at constant pressure of an ideal gas is (9/2)R. The ratio of specific heat at constant pressure to that at constant volume is

A)
1.58

B)
1.82

C)
1.28

D)
1.44
View Solution
94)

For a certain gas the ratio of specific heats is given to be y = 1.5. For this gas

A)
\[{{C}_{V}}=3R/J~\]

B)
\[{{C}_{p}}=3R/J\]

C)
\[{{C}_{p}}=5R/J\]

D)
\[{{C}_{V}}=5R/J\]
View Solution
95)

One mole of a diatomic gas is taken through the process \[P{{V}^{n}}=k,\] where n and k are constant. If the heat capacity of gas is negative, then the value of n may be

A)
\[\frac{5}{7}\]

B)
\[-\frac{5}{7}\]

C)
\[\frac{9}{7}\]

D)
\[-\frac{9}{7}\]
View Solution
96)

The relation between internal energy U, pressure P and volume V of an ideal gas in an adiabatic process is \[U=1+3PV.\]What is the value of the ratio of the molar specific heats \[\left( \frac{{{C}_{p}}}{{{C}_{V}}} \right)\]=?

A)
2/3

B)
4/3

C)
3/2

D)
1
View Solution
97)

Find the value of \[\gamma =\frac{{{C}_{p}}}{{{C}_{V}}}\] for a mixture consisting of \[{{n}_{1}}\] moles of a monoatomic gas and \[{{n}_{2}}\] moles of a gas of diatomic molecules:

A)
\[\frac{{{n}_{1}}}{{{n}_{2}}}\]

B)
\[\frac{5{{n}_{1}}+7{{n}_{2}}}{3{{n}_{1}}+5{{n}_{2}}}\]

C)
\[\frac{3{{n}_{1}}+5{{n}_{2}}}{5{{n}_{1}}+7{{n}_{2}}}\]

D)
\[\frac{7{{n}_{1}}+3{{n}_{2}}}{5{{n}_{1}}+3{{n}_{2}}}\]
View Solution
98)

Graph of specific heat at constant volume for a monatomic gas is

A)

B)
(b)

C)

D)

View Solution
99)

The K.E. of one mole of an ideal gas is E=(3/2) RT. Then \[{{C}_{p}}\]will be

A)
0.5 R

B)
0.1 R

C)
1.5 R

D)
2.5 R
View Solution
100)

For a gas sample with Np number of molecules, function N(V) is given by: \[N\left( V \right)=\frac{dN}{dV}=\left[ \frac{3{{F}_{0}}}{V_{0}^{3}} \right]{{V}^{2}}\] for \[0\le V\le {{V}_{0}}\]and \[N\left( V \right)=0\]for \[V>{{V}_{0}}\] Where \[dN\] is number of molecules in speed range V to \[V+dV.\]The rms speed of the gas molecule is

A)
\[\sqrt{\frac{2}{5}}{{V}_{0}}\]

B)
\[\sqrt{\frac{3}{5}}{{V}_{0}}\]

C)
\[\sqrt{2}{{V}_{0}}\]

D)
\[\sqrt{3}{{V}_{0}}\]
View Solution

Study Package

Self Evaluation Test - Kinetic Theory

Buy Now

JEE Main & Advanced Physics Kinetic Theory of Gases Question Bank

done Self Evaluation Test - Kinetic Theory Total Questions - 100

Study Package

Self Evaluation Test - Kinetic Theory

Self Evaluation Test - Kinetic Theory Total Questions - 100