Important Problems on Kinetic theory of gases

Question 1.
Calculate the volume of 3 mole of an ideal gas at STP

Question 2
Calculate the mass of 4 cm3 of nitrogen at STP

Question 3
Equal masses of air are filled and sealed in two container ,one of volume V0 and other of the volume 4V0.If the first vessel is maintained at 200K and other at 800K.Find the ratio of the pressure in the two containers

Question 4
An glass bulb of volume 390 cc was sealed at a pressure of 2*10-3 mm of mercury at 25° C. Compute the number of the air molecules in the bulb .Avogadro number=6 x 1023 per mole, Density of mercury=13600Kg/m3
g=10 m/s2

Question 5
A gas container has a walls that can bear maximum pressure of 2.2 x 106 pa.The container contains gas at 4 x 105 pa and 350K.If the container is steadily heated then neglecting change in volume, Calculate the temperature at which container will break?

Question 6
Density of an ideal gas at STP is 3 x 10-3 gm/cm3.Calculate the Molecular Weight of the gas

Question 7
A vessel of volume V=30 L contains ideal gas at temperature 0° C. After the portion of gas has been let out, the pressure in the vessel decreased by ΔP=.78 atm(Temp remaining constant).Find the mas of the gas released. The gas density under normal condition is ρ=1.3 g/L

Question 8
A vessel of volume V=20L contains a mixture of hydrogen and helium at T=20° C and Pressure P=2.0 atm.The mass of the mixture is equal to m=5g.Find the ratio of the mass of the hydrogen to that mass of the helium in the mixture. Given R=.082 L.atm.mol-1.K-1

Question 9
Find the rms speed of the hydrogen molecules in a sample of hydrogen gas at 250K .Find the temperature at which rms speed is three times the speed at 250K

Question 10
An ideal gas sample of .203 gm occupies 1000 cm3 at STP.Calculate the RMS speed of the molecules

Question 11
The mean speed of the molecules of a hydrogen sample equals the mean speed of the molecules of helium sample. Calculate the ratio of temperature of hydrogen sample to the temperature of the helium sample.

Question 12
Find the ratio of the mean speed of the hydrogen molecule to the mean speed of the oxygen molecules in a sample containing mixture of two gases

Question 13
A vessel is partitioned by a fixed diathermic separator. Different ideal gases are filled in the two parts. The rms speed of the molecules in the left part equals the mean speed in the right part. Calculate the ratio of the mass of the molecule in the left part to the mass of the molecule in the right part?

Question 14
An air bubble of radius 3.00 mm is formed at the bottom of the 4 m deep river. Calculate the radius of the air bubble as it comes to the surface .Atmospheric pressure=105 Pa and density of the water=1000 kg/m3

Question 15
Air is pumped into the tubes of a cycle at 1.5 atm pressure and volume of tube at this pressure is .002 m3.When one of the tubes get punctured volume of tube reduces to .0004 m3. Calculate the number of moles that leaked from the tube assuming that air is an ideal gas and temperature remains constant at 300K.

Question 16
A tank attached to an air compressor contains 30L of air at temperature of 40° C and gauge pressure 5*105 pa. What is the mass of the air and what volume would it occupy at normal atmosphere pressure

Question 17
Figure below shows two vessels A and B with rigid walls containing ideal gases. The pressure ,temperature and volume are PA,TA,V in vessel A and PB,TB,V in vessel B.Th. vessels are now connected through a small tube .Show that the pressure P and Temperature T satisfy
P/T=1/2[PA/TA + PB/TB]
when equilibrium is reached

Question 18
Figure shows a cylindrical tube of length 30 cm partitioned by a tight fitting separator.The separator is weekly conducting and can freely slide along the tube. Ideal gases are filled in the two parts of the vessel. In the beginning, temp in two parts A and B are 400K and 100 K respectively. The separator slides to a momentary equilibrium position as shown in fig.Find the equilibrium position of the separator reached after the long time

Assertion and Reason
a) Statement I is true ,statement II is true ,statement II is correct explanation for statement I
b) Statement I is true ,statement II is true ,statement II is not a correct explanation for statement I
c) Statement I is true,Statement II is false
d) Statement I is False,Statement II is True
Question 19
STATEMENT 1:The root mean square velocity of molecules of a gas having Maxwellian distribution of velocities is higher than then the most probable speed at any temperature
STATEMENT II:A very small number of molecules of as gas which possess very large velocities,increase the root mean square velocity without effecting the most probable speed.

Question 20
STATEMENT 1:Root mean square velocity of the gas does not change in a Isothermal process
STATEMENT 2:Isothermal process may be achieved by immersing the system in large reservoir and performing the process slowly

Question 21
STATEMENT 1:In an gas $v_{rms} > v_{mean}$
STATEMENT 2: In an gas $v_{rms} < v_{most probable}$

Question 22
STATEMENT 1:Thermal conduction is the heat transfer that occurs in the direction of temperature decrease
STATEMENT 2:Thermal conduction is solids occurs due to vibrational energy of the molecules about the equilibrium position

Question 23
Three identical cylinder $A_1$,$A_2$,$A_3$ contains equal moles of Helium,Nitrogen,Carbon dioxide at the same temperature
Match the column A to column B
Column A
A.Translational Energy is maximum in the cylinder
B.Total energy is minimum in the cylinder
C.Root mean square velocity is maximum in the cylinder
D.Mean speed will be minimum in the cylinder

Column B
P. $A_1$
Q. $A_2$
R. $A_3$
S. No appropriate match given

Question 24
Consider an ideal gas with following distribution of speeds

(i) Calculate $V_{rms}$ and hence T. (m= 3.0 × 10-26 kg)
(ii) If all the molecules with speed 1000 m/s escape from the system, calculate new $V_{rms}$ and hence T.
$K_b= 1.38 \times 10^{-23}$

Question 25
An ideal gas sample of .203 gm occupies 1000 cm3 at STP. Calculate the RMS speed of the molecules

Question 26
How will the rate of collision of a rigid diatomic molecules against the vessel will change ,if the gas is expanded adiabatically η times