Kinetic Theory Of Gases MSQ - IIT JAM MCQ

According to the problem, mass of gases are equal so number of moles will not be equal i.e.  
From ideal gas equations :   

∴ 
(∴ temperature of container are equal)
From this relation, it is clear that if p_A = p_B then 
Similarly if V_A = V_B then  i.e. p_A ≠ p_B.
The correct answers are:  
 

We know that 


so, 

∴  Average kinetic energy 

The correct answers are:  The average kinetic energy of a molecule is 

At low pressure and high temperature real gas obey pV = RT i.e. they behave as ideal gas because at high temperature we can assume that there is no force of attraction or repulsion works among the molecules and the volume occupied by the molecules is negligible in comparison to the volume occupied by the gas.
The correct answers are: Low pressure, High temperature

The rms speed depends upon the molecular mass.  but kinetic energy does not depend on it.
i.e.  
On the problem 
∴ 
But  
The correct answers are: 

As  i.e. mean free path is inversely proportional to density of a gas. As 
For constant volume and thus constant number density n of gas molecule. P/T is constant so, λ will not depend on p and T.
But if volume of given mass of a gas is allowed to change with p and T, then   at constant pressure and  at constant temperature.
The correct answers are: Mean free path is inversely proportional to density of gas, For constant volume,  will not depend on T and p

For state A, C_p - C_V = R i.e. gas behaves as ideal gas. For state B, C_p – C_v = 1.06R ≠ R i.e. gas does not behave like ideal gas, and we know that at high temperature and at low pressure nature of gas may be ideal so we can say that p_A < p_B and T_A > T_B .
The correct answers are: p_A < p_B , T_A > T_B

Initially for container A,

For container B, p₀ V₀ = n₀ RT₀
∴ 
Total number of moles =  n₀ + n₀ = 2n₀
Since even on heating, total number of moles is conserved, hence
n₁ + n₂ = 2n₀ .....(1)
If p be the common pressure, then for container A,
pV₀ = n₁ R2T₀
⇒ 
For container B, 
⇒ 
Substituting the value of n₀ , n₁ and n₂ is equation (1), we get
⇒ 
Number of mole in container A (at temperature 2T₀ )

The correct answers are: 

⇒ 
⇒ 
Compairing thus with    p = AV^m – BVⁿ
we get m = –c and n = –1.
The correct answers are:
m = -c,
n = –1

At absolute temperature, kinetic energy of gas molecules becomes zero but they possess potential energy so we can say that at absolute zero degree temperature is not zero energy temperature.
The correct answers are: Two different gases at the same temperature and pressure have equal root mean square velocities, The rms speed of the molecules of different ideal gases, maintained at some temperature are the same, Given sample of ice of hydrogen and ice of oxygen both at NTP oxygen sample has a large number of molecules