Diatomic molecules like hydrogen have energies due to both translational as well as rotational motion. From the equation in kinetic theory PV=23E, E is:
the total energy per unit volume.
only the translational part of energy because rotational energy is very small compared to the translational energy.
only the translational part of the energy because during collisions with the wall, pressure relates to change in linear momentum.
the translational part of the energy because rotational energies of molecules can be of either sign and is average over all the molecules is zero.
When an ideal gas is compressed adiabatically, its temperature rises and thus, the molecules on the average have more kinetic energy than before. The kinetic energyincreases:
because of collisions with moving parts of the wall only.
because of collisions with the entire wall.
because the molecules gets accelerated in their motion inside the volume.
because of redistribution of energy amongst the molecules.
In a diatomic molecule, the rotational energy at a given temperature:
(a) obeys Maxwell’s distribution
(b) have the same value for all molecules
(c) equals the translational kinetic energy for each molecule
(d) is (2/3)rd the translational kinetic energy for each molecule
(a, b)
(a, d)
(c, d)
(a, c)
Which of the following diagrams (figure) depicts ideal gas behaviour?
A cubic vessel (with faces horizontal + vertical) contains an ideal gas at NTP. The vessel is being carried by a rocket which is moving at a speed of 500 ms-1 in vertical direction. The pressure of the gas inside the vessel as observed by us on the ground:
remains the same because 500 ms-1 is very much smaller than Vrms of the gas.
remains the same because the motion of the vessel as a whole does not affect the relative motion of the gas molecules and the walls.
will increase by a factor equal to V2rms+500V2rms where Vrms was the original mean square velocity of the gas.
will be different on the top wall and bottom wall of the vessel.
Boyle's law is applicable for an:
adiabatic process
isothermal process
isobaric process
isochoric process
A cylinder containing an ideal gas is in a vertical position and has a piston of mass M that is able to move up or down without friction (figure). If the temperature is increased,
both P and V of the gas will change.
only P will increase according to Charles' law.
V will change but not P.
P will change but not V.
The volume versus temperature graphs for a given mass of an ideal gas are shown in the figure at two different values of constant pressure. What can be inferred about relation between P1 and P2?
P1>P2
P1=P2
P1<P2
Data is insufficient
1 mole of H2 gas is contained in a box of volume V = 1.00 m3 at T = 300 K. The gas is heated to a temperature of T = 3000 K and the gas gets converted to a gas of hydrogen atoms. The final pressure would be: (considering all gases to be ideal)
same as the pressure initially
2 times the pressure initially
10 times the pressure initially
20 times the pressure initially
A vessel of volume V contains a mixture of 1 mole of hydrogen and 1 mole of oxygen (both considered as ideal). Let f1(v)dv denotes the fraction of molecules with a speed between v and (v+dv) with f2(v)dv similarly for oxygen. Then,
f1(v)+f2(v) = f(v) obeys the Maxwell's distribution law
f1(v), f2(v) will obey the Maxwell’s distribution law separately
neither f1(v), nor f2(v) will obey the Maxwell’s distribution law
f2(v) and f1(v) will be the same
An inflated rubber balloon contains one mole of an ideal gas, has a pressure p, volume V and temperature T. If the temperature rises to 1.1T, and the volume is increased to 1.05V, the final pressure will be:
1.1p
p
less than p
between p and 1.1p
ABCDEFGH is a hollow cube made of an insulator (figure). Face ABCD has a positive charge on it. Inside the cube, we have ionised hydrogen. The usual kinetic theory expression for pressure:
(a) will be valid
(b) will not be valid, since the ions would experience forces other than due to collisions with the walls
(c) will not be valid, since collisions with walls would not be elastic
(d) will not be valid because isotropy is lost
(b, d)
The mean free path l for a gas molecule depends upon the diameter, d of the molecule as:
l ∝1d2
l ∝d
l ∝ d2
l ∝1d
The density of water is 1000 kg m–3. The density of water vapour at 100 °C and 1 atm pressure is 0.6 kg m–3. The volume of a molecule multiplied by the total number gives, what is called, molecular volume. The ratio (or fraction) of the molecular volume to the total volume occupied by the water vapour under the above conditions of temperature and pressure is:
5×10-4
60×10-4
50×10-4
6×10-4
The density of water is 1000 kg m–3. The volume of a water molecule is:
4×10-29 m3
4×10-28 m3
3×10-29 m3
3×10-29 cm3
The density of water is 1000 kg m–3. The density of water vapour at 100 °C and 1 atm pressure is 0.6 kg m–3. What is the average distance between molecules (intermolecular distance) in water? (Given, the diameter of a water molecule in liquid state = 4 Aο)
47.45 Aο
37.34 Aο
20.23 Aο
50.45 Aο
A vessel contains two nonreactive gases: neon (monatomic) and oxygen (diatomic). The ratio of their partial pressures is 3:2. The ratio of the number of molecules is:
(Atomic mass of Ne = 20.2 u, molecular mass of O2 = 32.0 u)
2:3
3:2
1:3
3:1
A vessel contains two nonreactive gases: neon (monatomic) and oxygen (diatomic). The ratio of their partial pressures is 3:2. The ratio of mass density of neon and oxygen in the vessel is: (Atomic mass of Ne = 20.2 u, molecular mass of O2 = 32.0 u).
0.397
0.937
0.947
1
A flask contains argon and chlorine in the ratio of 2:1 by mass. The temperature of the mixture is 27 °C. The ratio of average kinetic energy per molecule of the molecules of the two gases is:
(Atomic mass of argon = 39.9 u; Molecular mass of chlorine = 70.9 u)
1:2
2:1
1:1
A flask contains argon and chlorine in the ratio of 2:1 by mass. The temperature of the mixture is 27 °C. The ratio of root mean square speed vrms of the molecules of the two gases is:
2.33
1.33
0.5
2
Uranium has two isotopes of masses 235 and 238 units. If both are present in Uranium hexafluoride gas, which would have the larger average speed?
UF6235
UF6238
Both will have the same average speed.
Data insufficient
Uranium has two isotopes of masses 235 and 238 units. If both are present in Uranium hexafluoride gas. If the atomic mass of fluorine is 19 units, what is the percentage difference in speeds of isotopes of Uranium at any temperature?
0.43%
0.34%
0.55%
When a molecule (or an elastic ball) hits a ( massive) wall, it rebounds with the same speed. When a ball hits a massive bat held firmly, the same thing happens. However, when the bat is moving towards the ball, the ball rebounds at a different speed. Does the ball move faster or slower?
Faster
Slower
Speed of ball does not changes
None of these
A cylinder of fixed capacity 44.8 litres contains helium gas at standard temperature and pressure. What is the amount of heat needed to raise the temperature of the gas in the cylinder by 15.0 °C? (R = 8.31 J mol–1 K–1).
The diameter of the water vapour molecule is 2×10-10 m and the number of molecules per unit volume at STP is 2.7×1025 m-3. The mean free path for a water molecule in water vapour at 373 K is:
2.5×10-7 m
6×10-7 m
3×10-7 m
4×10-7 m
Match column - I and column - II and choose the correct match from the given choices.
(A) - (Q), (B) - (P), (C) - (S), (D) - (R)
(A) - (R), (B) - (Q), (C) - (P), (D) - (S)
(A) - (R), (B) - (P), (C) - (S), (D) - (Q)
(A) - (Q), (B) - (R), (C) - (S), (D) - (P)
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