Kinetic Theory of Gases Questions and Answers

A B 300K 400K Vapour pressure of liquid at 300 K is 20 mm of Hg and 400 K is 40 mm of Hg Very long time after opening the stopper the total pressure will be 1 20 mm of Hg 2 40 mm of Hg 3 30 mm of Hg 4 50 mm of Hg

Sri Chait 32 Sr IPLCO JEE ADV 2011 P1 RPTA 15 Q Paper Which of the following is true with regards to the below graph of the Maxwell speed distribution for the molecules of an ideal monatomic gas at 300K N IN dN N v in 10 s m 2 0 1 0 0 0 200 Fav Vp Veme 400 600 dv Area N v dv 800 1000 1200 Speed m s A N v represents the number of molecules having speed v B The probability that a molecule has a precisely stated speed such as 600 34326759 m s is finite The number of molecules whose speeds lie in a narrow range such as 600 m to 10000 m s has a definite non zero value D Area under the graph given by N v dv represents the total number of molecules in the system

N molecules is 14 times heavier than a H2 molecule At what temperature will the rms speed of H molecules be equal to that of N2 molecule at 27 C Question Type Single Correct Type 1 50 C 2 40 C 3 87 C

edieval Two different ideal diatomic gases A and B are initially in the same state A and B are then expanded to same final volume through adiabatic and isothermal process respectively If PA PB and TA TB represents the final pressure and temperatures at A and B resepectively then a PA PB and T TB TA c PA PB and T TB b PA PB and TA TB d PA PB and TA TB clic process ABCDA shown in the figure

2 1 5 R 3 2R 4 2 5 R Consider a thermodynamic system which ge from 1 to f through the process shown figure here Then work is done Pressure Volume 1 By the system through out the path iABf 2 By the system for path iAB and on the system for path Bf

8 A certain ideal gas with adiabatic exponent y 1 5 is isothermally compressed to half its initial volume Find the further fractional change in pressure isochorically such that when the gas is adiabatically expanded it reaches its initia conditions 1 0 41 3 0 51 20 PAS 2 0 73 4 4 0 49

The molar heat capacity C of an ideal gas in a process is given by where a is constant y work done by one mole of gas during heating from To to n To through the same process will be A logn C D a logn 1 To a logn y 1 RTO RTO

the mass of a suspended particle is 10 kg calculate Vrms Calculate the probability that the speed of an oxygen molecule will lie between 100 m s and 101 m s at 200 K The mass of oxygen molecule is 32 u Take kB 1 38 x 10 23 J K and NA 6 x 1026 k mol

A vessel contains two non reactive gases monoatomic neon and diatomic oxygen The ratio of their partial pressure is 5 3 Estimate the ratio of number of moles of neon and oxygen in a vessel Molar mass oxygen O 32 0 u and atomic mass of neom NCERT Pg 322 20 2 u 1 5 3 2 3 5 3 4 3

aximum density at 4 C 5 Coefficient of volume expansion of ideal gases at constant pressure and at temperature TK is equal to 1 2 T 3 7 1 2 4 T r NCERT Pg 2821 kas Fou

0 A cylinder of capacity 44 8 litres contains helium gas at standard temperature and pressure What amount of heat is needed to raise the temperature of gas in cylinder by 10 C NCERT Pg 335 1 173 5 J 2 249 3 J 3 205 2 J 4 374 2 J

One litre of oxygen at a pressure of 1 atm and two litre of nitrogen at a pressure of 0 5 atm are introduced into a vessel of volume one litre If there is no change in temperature the final pressure of the mixture of the gases in atm is A 1 5 B C 2 5 2 Correct Answer

ALLEN Two spherical vessel of equal volume are 40 connected by a narrow tube The apparatus contains an Ideal gas at one atomosphere and 300 K Now if one vessel is immersed in a bath of constant temperature 600 K and other in a bath of contant temperature 300 K Then the common pressure will be 1 1 atm atm A 2 In atm atm If C and C denote the specific heats of nitrogen 41 afcient art targeta da 300 fe fe a 600 K and 1 1 atm a 300 fa a 3 atm ufe C 3 C 2 45 34 B atm atm

ALLEN 17 mar Which of the following statements is true 1 Absolute zero temperature is not zero energy temperature 2 Two different gases at the same temperature pressure have equal root mean square velocities 3 The rms speed of the molecules of different ideal gases maintained at the same temperature are the same 4 Given sample of Icc of hydrogen and Ice of oxygen both at N T P oxygen sample has a large number of molecules An ideal gas is taken through the cycle ABC 18 1 2 3 fatims 4 NTP Ice Ice yf en at the fear B C

A gaseous mixture was prepared by taking equal moles of CO and N If the total pressure of the mixture was found 1 atmosphere the partial pressure of the nitrogen N in the mixture is a 0 5 atm b 0 8 atm d 1 atm c 0 9 atm 2011

The following condition is satisfied by two different gases A and B TAMB TBMA Where MA and MB represents molar mass of A and B respectively and MA MB TA and T are temperatures of A and B respectively and T TB A The property which can never have same magnitude for both gases V velocity 1 Vrms 2 V mp 101

One mole of an ideal monoatomic gas degree of freedom 3 2 moles of an ideal diatomic gas degree of freedom 5 and 3 moles of an ideal triatomic gas degree of freedom 6 are mixed Yeg for the mixture a is Here a and are integers Find the a 2 minimum value of

5 R R Which one of the following methods will enable the volume of ideal gas to be increased four times 4 1 Double the temperature and reduce the pressure to half 2 Double the temperature and also double the pressure 3 Reduce the temperature to half and double the pressure 4 Reduce the temperature to half and reduce the pressure to half

D The mean free path of benzene molecule is 6 x 10 6 m and average speed of molecules is 1 2 x 10 m s The collision rate of molecules is ON 1 3 x 107 s 1 3 4 x 107 s 1 vlev 2 4 x 108 s 1 4 2 x 108 S 1

Q8 Oxygen and hydrogen gases are at temperature T Then K E of molecules of oxygen gas is equal to how many times of K E of molecules of hydrogen gas a 16 times b 8 times c Equal d 1 16 times

et the r m s velocity of molecule of a given mass of gas be C at temperature 27 C When th emperature is increased to 327 C the r m s velocity of C Then the ratio C2 is C A B 4 meg C 2 D 2 2

For a gas molecule its degree of freedom for translation is 3 for rotation is 2 and for vibration is 2 If its rotational K E KER is related to total energy E by KER nE then n would be 1 3 2 2 7 2 3 3 7 4 2 7

Figure shows three vessels A B and C of same volume connected by tubes of very small volume with two valves P P2 The pressure temperature and no of moles of monoatomic gas filled in A are 2Po To 4n and Po 2To n in vessel C but gas is diatomic In vessel B vacu m is created 03 Now valves p and p2 are opened Find final temperature in Kelvin of mixture when equilibrium is achieved If the heat loss to atmosphere in this process is 650 R Joule Given Po 18 105 N m To 300 K n 2

Match List I with List II List I i A Isothermal B Isochoric ii Temperature constant C Adiabatic iii Volume constant D Isobaric iv Heat content is constant Choose the correct answer from the options given below List II Pressure constant a A i B iii C ii D iv b A iii B ii C i D iv c A ii B iii C iv D i d A ii B iv C iii D i

temperature In Maxwell s speed distribution curve on increasing the number of gas molecules having most probable speed 1 Decreases TE 2 Increases 3 May increase or decrease 4 Remains constant

An ideal gas is compressed to half its initial volume by means of several processes Which of the process results in the maximum work done on the gas Re Test 2015 A Isothermal B Adiabatic C Isobaric D Isochoric

The strength of magnetic field required to bend photoelectrons of maximum energy in a circle of radius 50 cm when light of wavelength 3300 is incident on a barium emitter is 6 7 x 10 6 T The value of charge on the photoelectrons is obtained from this data is Given Work function of barium 2 5 eV mass of the electron 9 10 31 kg Question Type Single Correct Type 1 0 6 10 10 C 2 1 8 x 10 19 C 3 0 6 x 10 12 C A 18 x 10 20

A container has an ideal gas at pressure P in thermal equilibrium Assuming the mass of a molecule is Im and all the molecules are moving with same speed v in random directions The expression for number of collisions per second which the molecules make with unit area of container wall is Question Type Single Correct Type 1 2 3 P mv 3P 2mv 3P 2mv 3P

0 Two vessels having equal volumes contains molecular hydrogen at 1 atmospheric pressure and helium at 2 atmospheric pressure If both samples are at same temperature the r m s velocity of the hydrogen molecule is 1 Equal to that of helium molecule 2 Half of that of helium molecule 3 2 times that of helium 4 2 times that of helium

A cylinder containing gas at 27 C is divided into two parts of equal volume each 100cc and at equal pressure by a piston of cross sectional area 10 85 cm The gas in one part is raised in temperature to 100 C while the other maintained at original temperature The piston and wall are perfect insulators How far will the piston move during the change in temperature Question Type Single Correct Type 1 1 cm 22 cm 3 0 5 cm 4 1 5 cm

1 mole of H gas is contained in a box of volume V 1 00 m a T 300K The gas is heated to a temperature of T 3000K an the gas gets converted to a gas of hydrogen atoms The fina pressure would be considering all gases to be ideal a same as the pressure initially b 2 times the pressure initially c 10 times the pressure initially d 20 times the pressure initially

A balloon contains 1500 m of helium at 300 K and 4 atmospheric pressure The volume of helium at 270 K and 2 atmospheric pressure will be Assuming no leakage of gas 1 1500 m 3 1700 m NCERT Pg 321 2 1900 m 4 2700 m3

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

5 7 A vessel of volume V contains a mixture of 1 mole of Hydrogen and 1 mole of Oxygen both considered as ideal Let f v du denote the fraction of molecules with speed between vand v du with v du similarly for oxygen Then a f v f v f v obeys the Maxwell s distribution law b f u f v will obey the Maxwell s distribution law separately c Neither f v nor f v will obey the Maxwell s distribution law d f u and f v will be the same

B P F D H 13 9 C G ABCDEFGH is a hollow cube made of an insulator Fig 13 4 Face ABCD has positve charge on it Inside the cube we have ionized 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

1 a Two hydrogen ions of a water molecule form an angle of 104 5 with the oxygen ion Each O H bond length is 0 096 nm a Find the Coulomb force on the oxygen atom b Find the electric field at the location of oxygen

The van der Waal s equation of state for some gases can be expressed as P V b RT Where P is the pressure V the molar volume and T is the absolute temperature of the given sample of gas a b and R constant The dimensions of b are 1 ML T 2 3 1 2 ML T 21 4 L 27 28

An ideal diatomic gas under goes a process in which internal energy changes with volume as given U CV5 Where C is constant Find the ratio of molar heat capacity for this process to universal gas constant R A slightly tapering wire of length e and end radii a and b is subjected to

Two identical heaters are coated with paint In 1st case e 1 0 and in 2nd case e2 0 5 Both are kept in identical chambers which are in similar surroundings If the heaters are switched on in steady state 1st heater has temperature T on surface and 0 of its chamber 2nd heater has temperature T2 on surface and 02 of its chamber Then select the correct option s Question Type Multiple Correct Type 1 2 3 0 02 T1 T2 01 02

For the two adiabatics shown on a pressure volume P V diagram if process 1 is for oxygen gas then process 2 may be for Assume all gases are ideal 1 N PA V 2 CO

For an ideal gas if the ratio of Molar specific heats y 1 4 then the specific heat at constant pressure Cp specific heat at constant volume C and corresponding molecule are respectively 5 3 0 R 1 1 1 A 2 2 B C 7 2 9 R R 5 2 7 2 R monoatomic R polyatomic R non rigid diatomic 7 DER 51 R R rigid diatomic

An ideal gas has initial volume V and pressure P To triple its volume the minimum work done will be in NCERT Pg 312 1 Isothermal process 2 Adiabatic process 3 Isobaric process 20 11 16 10 33000 4 Equal in all process 19 dodal ns 107

The cyclic process ABCDA has been performed on helium gas which behaves ideally Process AB is isothermal and CD is adiabatic The ratio of maximum to minimum temperature in complete cycle is 4 Find the change in internal energy in the process CD in terms of P and V PA A P Pot D C B V 82V 3 2 Po V

CH B 14 Two flasks A and B made of conducting materials are connected by a thin tube Two valves C and D are installed on the tube as shown in the figure Initially both the flasks are evacuated and the valves are closed Now the valve D is opened an ideal gas is filled in the flask B at pressure p and then the valve D is closed When the valve C is opened the pressure in the flask B drops by amount Ap If volume of the flask B is VB what is the volume of the flask A a c ApVB p Ap p Ap VB p b d PV p Ap P AP VB Ap

lasch Column 1 and Column 1 and che correct match frian the given choices Column 1 Column 11 A Root mean equame od of gue mol enles Per exerted by ideal ga 1 KB Average kinetic energy 00 of a molecule mil VM RT 20 D Total internal energy 1 mole of a distomic gas 3 10 B Q C 05 b 8 A R H P C 15 0 0 B C s p

Two vessels separately contain two ideal gases A and B at the same temperature The pressure of A is 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 weights of A and B is A 2 B C 3 12 22

Container x has volume doubled that of container y are connected by thin tube Both contains same ideal gas The temperature of x is 200 K and that of y is 400 K If mass of gas in x is m then in y it will be 1 m 8 3 m 4 A 1 2 m 6 4 m 2

12 A cylindrical box is moving with a constant velocity along its axis in a chamber filled with an ideal gas Velocity of the cylinder is so small that it does not produce any turbulence in the gas If absolute temperature of the gas is doubled in what way must speed of the cylinder be changed to keep the drag force unchanged a It must be made 0 354 times of its previous value b It must be reduced to half of its previous value c It must be made 0 707 times of its previous value d Drag force does not depend on the temperature of the gas

SolveLancer Test In a cylindrical vessel with frictionless piston 5 moles of a diatomic gas expand adiabatically until its volume gets doubled The gas is initially at 106 N m and 300 K Calculate the work done in expansion SolveLancer Test a 2764 J b 7574 J c 5574 J d 3764 J Da Ob

2 8 In a cubical box of volume V there are N molecules of a gas moving randomly If m is mass of each molecule and is the mean square of x component of the velocity of molecules then the pressure of the gas is 1 mNv 3 V 1 P 1 3 P mNz1 2 P mNv V 4 P mN7