Q1: The temperature of a gas is –50°C. To what temperature the gas should be heated so that the rms speed is increased by 3 times? [2023]
(a) 669°C
(b) 3295°C
(c) 3097 K
(d) 223 K
Ans: (b)
T_{1} = 273− 50
= 223 K
vrms is increased by 3 times
T_{2} = ?
So, final rms speed = v + 3v = 4v
Q1: Match column  I and column  II and choose the correct match from the given choices. [2021]
(a) (A)  (Q), (B)  (P), (C)  (S), (D)  (R)
(b) (A)  (R), (B)  (Q), (C)  (P), (D)  (S)
(c) (A)  (R), (B)  (P), (C)  (S), (D)  (Q)
(d) (A)  (Q), (B)  (R), (C)  (S), (D)  (P)
Ans: (a)
Root mean square speed of gas molecules
Q1: A cylinder contains hydrogen gas at pressure of 249 kPa and temperature 27°C.
Its density is : (R = 8.3 J mol^{1} K^{1}) [2020]
(a) 0.1 kg/m^{3}
(b) 0.02 kg/m^{3}
(c) 0.5 kg/m^{3}
(d) 0.2 kg/m^{3}
Ans: (d)
∴ PV = nRT
Q2: The mean free path for a gas, with molecular diameter d and number density n can be expressed as : [2020]
(a)
(b)
(c)
(d)
Ans: (d)
The mean free path for gas is given by
Q3: The average thermal energy for a monoatomic gas is (k_{B} is Boltzmann constant and T, absolute temperature) [2020]
(a) 1/2k_{B}T
(b) 3/2k_{B}T
(c) 5/2k_{B}T
(d) 7/2k_{B}T
Ans: (a)
For monoatomic gas, degree of freedom = 3
Energy associated with each degree of freedom = 1/2k_{B}T
So, energy is 3/2k_{B}T
Q1: Increase in temperature of a gas filled in a container would lead to: [2019]
(a) Increase in its mass
(b) Increase in its kinetic energy
(c) Decrease in its pressure
(d) Decrease in intermolecular distance
Ans: (b)
Solution: Increase in temperature would lead to the increase in kinetic energy of gas (assuming far as to be ideal) as
Q1: 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 × 10^{–26} kg Boltzmann's constant kB = 1.38 × 10^{–23} J K^{–1}): [2018]
(a) 2.508 × 10^{4} K
(b) 8.360 × 10^{4} K
(c) 5.016 × 10^{4} K
(d) 1.254 × 10^{4} K
Ans: (b)
Solution:
Q1: The deBroglie wavelength of a neutron in thermal equilibrium with heavy water at a temperature T(Kelvin) and mass m, is: [2017]
(a)
(b)
(c)
(d)
Ans: (a)
Solution: Kinetic energy of thermal neutron with equilibrium
Q2: A gas mixture consists of 2 moles of O_{2} and 4 moles of Ar at temperature T. Neglecting all vibrational modes, the total internal energy of the system is: [2017]
(a) 15 RT
(b) 9 RT
(c) 11 RT
(d) 4 RT
Ans: (c)
Solution:
Q1: The molecules of a given mass of a gas have r.m.s. velocity of 200 ms^{1} at 27°C and 1.0 x 10^{5} Nm^{2} pressure. When the temperature and pressure of the gas are respectively, 127°C and 0.05 x 10^{5}Nm^{2}, the r.m.s. velocity of velocity of its molecules in ms^{1} is; [2016]
(a) 100 / 3
(b) 100 √2
(c) 400 / √3
(d) 100√2 / 3
Ans:
Solution:
It is given that,
v_{rms} = 200 m/s
T_{1} = 300 K
P_{1} = 10^{5} N/m^{2}
rms velocity of gas molecules,
For two different cases,
It is given that,
v_{rms} = 200 m/s
T_{1} = 300 K
P_{1} = 10^{5} N/m^{2}
rms velocity of gas molecules,
For two different cases,
Q2: 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 ? [2016]
(a) P/(kT)
(b) Pm/(kT)
(c) P/(kTV)
(d) mkT
Ans: (b)
As PV = nRT
or
This fits into the pattern , where n is the number of the degrees of freedom
Q2: 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) 2
(b) 1/2
(c) 2/3
(d) 3/4 [2015]
Ans: (d)
According to an ideal gas equation, the molecular weight of an ideal gas is
M = ρRT / P
where P, T and r are the pressure, temperature and density of the gas respectively and R is the universal gas constant.
∴ The molecular weight of A is
and that of B is
Hence, their corresponding ratio is
Q1: The mean free path of molecules of a gas,(radius ‘r’) is inversely proportional to: [2014]
(a) r
(b) √r
(c) r^{3}
(d) r^{2}
Ans: (d)
Solution:
102 videos411 docs121 tests

1. What is the Kinetic Theory of Gases? 
2. How does temperature affect the kinetic energy of gas particles? 
3. How does pressure relate to the Kinetic Theory of Gases? 
4. What is the root mean square speed of gas particles according to the Kinetic Theory of Gases? 
5. How does the Kinetic Theory of Gases explain the relationship between volume and pressure? 

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