JEE Main Physics - Kinetic Theory of Gases
Exam Duration: 60 Mins Total Questions : 30
The number of molecules in V litre of a gas NTP is
- (a)
\({N_0\over 22.4}\times V\)
- (b)
\({22.4\over N_0 }\times V\)
- (c)
\(N_0\times 22.4\over V\)
- (d)
\(N_0 \times V \times 22.4\)
Ratio of Vmp (most probable speed), Vav (average speed), Vrms (root mean square speed) of gas molecules are related as
- (a)
\(\sqrt{3}:\sqrt{2}:\sqrt{8\over \pi}\)
- (b)
\(2:\sqrt{3}:\sqrt{\pi\over8}\)
- (c)
\(\sqrt{2}:\sqrt{3}:\sqrt{8\over\pi}\)
- (d)
\(\sqrt{2}:\sqrt{8\over\pi}:\sqrt{3}\)
The root mean square velocity of gas molecules at 270 C is 1365 m/s.The gas is
- (a)
O2
- (b)
He
- (c)
N2
- (d)
CO2
1 kg of diatomic gas is at a pressure of 8x144Nm-2.The density of the gas is 4kgm-3.What is the energy of the gas due to its thermal motion?
- (a)
3x104J
- (b)
5x104J
- (c)
6x104J
- (d)
7x104J
If Cp and CV denote the specific heats of nitrogen per unit mass at constant pressure and constant volume respectively, then
- (a)
Cp-CV=\(R\over28\)
- (b)
Cp-CV=\(R\over14\)
- (c)
Cp-CV=R
- (d)
Cp-CV=2R
Which of the following gases possesses maximum rms velocity, all being at the same temperature?
- (a)
Oxygen
- (b)
Air
- (c)
Carbon dioxide
- (d)
Hydrogen
Hydrogen has maximum rms speed at NTP because:
- (a)
it is the lightest gas
- (b)
it absorbs heat rapidly
- (c)
it is a good conductor of heat
- (d)
it has only one electron in its atom
A sealed container with negligible thermal coefficient of expansion contains helium (a monoatomic gas). When it is heated from 300 K to 600 K, the average kinetic energy of helium atoms is:
- (a)
halved
- (b)
left unchanged
- (c)
doubled
- (d)
increases by a factor of \(\sqrt { 2 } \)
At a given volume and temperature the pressure of a gas:
- (a)
varies inversely as its mass
- (b)
varies inversely as the square of its mass
- (c)
varies linearly as its mass
- (d)
is independent of its mass
At what temperature the molecules of nitrogen will have the same rms velocity as the molecules of oxygen a 1270 C
- (a)
770C
- (b)
3500C
- (c)
2730C
- (d)
4570C
Two vessels A and B having equal volume contain equal Two vessels A and B having equal volume contain equal mark the correct statement.
- (a)
The pressure exerted by hydrogen is half that exerted by helium.
- (b)
The pressure exerted by hydrogen is half that exerted by helium.
- (c)
Average KE of the molecules of hydrogen is half the average KE of the molecules of helium.
- (d)
The pressure exerted by hydrogen is twice that exerted by helium.
To expel half the mass of air from a large flask at 27° C it must be heated to:
- (a)
540C
- (b)
1770C
- (c)
2770C
- (d)
3270C
A container has N molecules at absolute temperature T. If the number of molecules is doubled but kinetic energy in the box remains the same as before, the absolute temperature of the gas is:
- (a)
T
- (b)
T/2
- (c)
2T
- (d)
zero
The mass of oxygen gas occupying a volume of 11.2 litres at a temperature 27°C and a pressure of 760 mm of mercury is: (molecular weight of oxygen = 32)
- (a)
0.001456 kg
- (b)
0.01456 kg
- (c)
0.1456 kg
- (d)
1.1456 kg
Half a mole of helium at 27° C and at a pressure of 2 atmosphere is mixed with l.5 mole of Nj at 77° C and at a pressure at 5 atmosphere so that the volume of the mixture is equal to the sum of their initial volumes. If the temperature of the mixture is 69° C, its pressure is:
- (a)
3.5 atm
- (b)
3.8 atm
- (c)
3.95 atm
- (d)
4.25 atm
The ratio of the total energy of all the molecules of one mole of O2 to the total energy of all the molecules of two moles of He at the same temperature is:
- (a)
2 : 1
- (b)
1 : 2
- (c)
5 : 4
- (d)
5 : 6
The root mean square velocity of the molecules in a sample of helium is 5/7th that of the molecules in a sample of hydrogen. If the temperature of hydrogen sample is O°C,
that of helium sample is about:
- (a)
O°C
- (b)
283 K
- (c)
0 K
- (d)
100OC
Two gases A and B having same pressure P, volume V and temperature T are mixed. If mixture has volume and temperature as V and T respectively, then the pressure of the mixture will be:
- (a)
4P
- (b)
3P
- (c)
2P
- (d)
P
At which of the following temperatures would the molecules of a gas have twice the average kinetic energy they have at 27° C?
- (a)
313°C
- (b)
373°C
- (c)
393°C
- (d)
586°C
The quantity PV/kT(k= Boltzmann's constant) represents:
- (a)
number of moles of the gas
- (b)
total mass of the gas
- (c)
number of molecules in the gas
- (d)
density of the gas
A graph is plotted with PV/T on y-axis and mass of the gas along x-axis for different gases. The graph is:
- (a)
a straight line parallel to x-axis for all the gases
- (b)
a straight line passing through origin with a slope having a constant value for all the gases
- (c)
a straight line passing through origin with a slope having different values for different gases
- (d)
a straight line parallel to y-axis for all the gases
If the pressure of an ideal gas contained in a closed vessel increased by 0.5%, the increase in temperature is 2 K. The initial temperature of the gas is:
- (a)
27°C
- (b)
127°C
- (c)
3000C
- (d)
4000C
In the process PV = constant, pressure (P) versus density (p) , graph of an ideal gas is:
- (a)
a straight line parallel to P-axis
- (b)
a straight line parallel to p-axis
- (c)
a straight line passing through origin
- (d)
a parabola
The mean square speed of 4 molecules of a gas having speeds 1,2,3 and 4 m/s is
- (a)
2.44 m/s
- (b)
7.5 m/s
- (c)
2.5 m/s
- (d)
9 m/s
The equation of state corresponding to 8 g of O2 is
- (a)
PV = 8RT
- (b)
PV = \(\frac { RT }{ 4 } \)
- (c)
PV = RT
- (d)
PV = \(\frac { RT }{ 2 } \)
The mass of'H2 molecule is 3.32 x 10-24 g .if 1023 hydrogen molecules per second strike 2 cm2 of wall at an angle of 45° with the normal, when moving with a speed of 105 cm/s, the cm/s, pressure exerted on the wall is nearly:
- (a)
1350 N/m2
- (b)
2350 N/m2
- (c)
3320 N/m2
- (d)
1660 N/m2
Two balloons are filled, one with pure He gas and other by air, respectively. If the pressure and temperature of these balloons are same, then the number of molecules per unit volume is:
- (a)
more in the He filled balloon
- (b)
same in both balloons
- (c)
more in air filled balloon
- (d)
in the ratio of I : 4
The phenomenon of Brownian movement may be taken as evidence of ;
- (a)
kinetic theory of matter
- (b)
electromagnetic theory of radiation
- (c)
corpuscular theory of light
- (d)
photoelectric phenomenon
An insulated box containing a diatomic gas of molar mass M is moving with a velocity u. The box is suddenly stopped. The resulting change in temperature is:
- (a)
\(\frac { { mv }^{ 2 } }{ 2R } \)
- (b)
\(\frac { { mv }^{ 2 } }{ 3R } \)
- (c)
\(\frac { { mv }^{ 2 } }{ 5R } \)
- (d)
\(\frac { 2{ mv }^{ 2 } }{ 5R } \)
The average momentum of a molecule in an ideal gas depends on:
- (a)
temperature
- (b)
volume
- (c)
molecular mass
- (d)
none of these