Kinetic Theory of Gases Questions and Answers

One mole of an ideal diatomic gas undergoes a transition from A to B along a path AB as shown in the figure 1 2 P kPa Question Type Single Correct Type 3 The change in internal energy of the gas during the transition is 20 kJ 20 J 5 2 4 V m 12 kJ 6 B

the r m velocity he r m s velocity of hydrogen molecules at temperature T is seven tim trogen molecules at 300 K This temperature T is Molecular weights of hydrogen trogen are 2 and 28 respectively A 1350 K B 1700 K ce C 1050 K D 2100 K ce

47 Pressure P volume V and temperature T for a AT BT2 certain gas are related by P V and B are constants The work done by the gas as its temperature change from T to 12 while pressure remaining constant is B a A T T b A T T B T2 T A c 72 7 12 13 B 3 B d A T T T T 3 where A

Two moles of an ideal monoatomic gas occupies a volume V at 27 C The gas expands adiabatically to a volume 2 V Calculate a the final temperature of the gas and b change in its internal energy A a 195 K b 2 7 kJ B C D a 189 K b 2 7 kJ a 195 K b 2 7 kJ a 189 K b 2 7 kJ J

If a diatomic molecule is not a rigid rotator then the value of molar specific heat at constant volume Cv is R universal gas constant 1 1 22 3 3 1 7R 2 2 9 R 2 3 5 R 2 4 9 R7

Modern vacuum pumps can evacuate vessel down to a pressure 4 0 x 10 5 atm at room temperature 300 K Taking R 8 3 JK mole 1 atm 105 Pa and NAvogadro 6 10 mole the mean distance between molecules of gas in an evacuated vessel will be of the order of A B C D 0 2 m 0 2 nm 0 2 cm 0 2 mm MY

6 moles get dissociated supplied is 1 250R 3 750R 1000R A vessel contains diatomic gas If half of gas dissociated into individual atom then find new value of degree of freedom by ignoring the vibrational mode and any further dissociation 9 1 7 3 remains same but 5 into atoms The heat 11 3 2 500R 4 2 4 11 7 13 3

1 mole of a gas with 7 7 5 is mixed with 1 mole of a gas with 7 5 3 then the value of y for the resulting mixture is A B 7 5 2 5

In an ideal gas at temperature T the average force that a molecule applies on the walls of a closed container depends on T as T9 A good estimate for q is A B 2

Two rigid boxes containing different ideal gases are placed on a table Box A contains one mole of nitrogen at temperature To while Box B contains one mole of helium at temperature 7 3 To The boxes are then put into thermal contact with each other and heat flows between them until the gases reach a common final temperature Ignore the heat capacity of boxes Then the final temperature of the gases Tf in terms of To is A B C 1 1 2 To T H TE 37 H To 1 7 10 Jhy N

The work done by all the forces on the system equals to change in its OPTIONS CLEAR SELECTION MARK FOR REVIEW OA Mechanical energy OB Potential energy C Kinetic energy

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 O Equal to that of helium molecule O Half of that of helium molecule O times that of helium times that of helium

18 Read the given statements and decide which is are correct on the basis of kinetic theory of gases 1 Energy of one molecule at absolute temperature is zero II r m s speeds of different gases are same at same temperature III For one gram of all ideal gas kinetic energy is same at same temperature IV For one mole of all ideal gases mean kinetic energy is same at same temperature a All are correct c IV is correct b I and IV are correct d None of these

An ideal gas occupies a volume V at a pressure P and absolute temperature T The mass of each molecule is m If K is the Boltzmann s constant then the density of gas is given by expression A B C KB T P m 3KB T 2 P m P m 2 KB T P m

7 Heat Q is supplied to a solid to raise its temperature T across its melting point TM and boiling point TB Which of the following graphs correctly represents the relation between heat supplied and temperature TM TM A C Ta Ta 10 1 1 TM B D T

4 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 NCERT Pg 335 7 10 C 1 173 5 J 2 249 3 J 3 205 2 J 4 374 2 J 6 conditions of t contains equal statement was At low pressure molecules are interaction is n the gas behav 2001 07 201

3 Average potential energy of molecules 4 Speed of the gas molecule 13 If three molecules have speeds of 2000 ms 1 1000 ms 1 and 500 ms the ratio of rms speed to average speed is NCERT Pg 325 1 1 14 2 0 92 3 1 78 4 1 71 17 1 1 16 2 2 1 x 1 3 1 92 x 4 0 92 x The ratio monoator 1 3 5 3 4 5

3 Four times 4 Remains same 12 Pressure of a gas at constant volume is proportional to NCERT Pg 325 1 Total internal energy of gas 2 Square of average kinetic energy of gas molecule 3 Average potential energy of molecules 4 Speed of the gas molecule 13 If three molecules have have speeds of 2000 ms 1 1000 ms 1 and 500 ms 1 the 2 2 3 10 3 2 4 1 4 1 8 x 1 16 Air has temperatu air is 28 8 1 1 16 2 2 1 x 3 1 92

A vessel contains a mixture of 1 mole of oxygen and 2 moles of nitrogen at 300 K The ratio of average rotational kinetic energy per O molecule to that of per N molecule is 1 1 1 2 1 2 3 2 1 4 depends on moment of inertia of two

A mixture of ideal gas contains 5 moles of monatomic gas and 1 mole of rigid diatomic gas initially at pressure Po volume Vo and temperature To If the gas mixture is adiabatically compressed to a volume then the correct statement s is are Given 2 2 2 3 232 9 2 R Vo 4 is gas constant A Adiabatic constant of the gas mixture is 1 6 BThe final pressure of the gas mixture after compression is in between 9P and 10P C The work W done during the process is 13RT D The average kinetic energy of the gas mixture after compression is in between 18RT and 19RTO

Discus the shape A sample of gas occupies 10 ltr under a pressure 1 atm what will be volume if the pressure is increase to 2 atm Assume that the temp of the gas sample dose not change

6 VITA Consider the following PV diagram for a monoatomic gas The ratio of work done by the gas to the change in internal energy of the gas will be P 2P P 1 1 3 3 Zero V 2V 2 3 1 4 1 1

Q 17 If at same temperature and pressure the densities for two diatomic gases are respectively d and d2 then the ratio of velocities of sound in these gases will be 1 d Vd 3 d d 2 4 d Vd 00 d d

Temperature versus pressure graph of an ideal gas is shown in the figure If density of gas at point P is p then density of gas at point Q will be P 4 Po Po 314 Pi To 3To T

At what temperature the root mean square speed of molecules of a gas is twice of its root mean square speed at 27 C 527 C 427 C 1127 C 927 C

Question No 13 At what temperature the root mean square speed of molecules of a gas is twice of its root mean square speed at 27 C O 527 C 427 C O 1127 C 927 C

6 Three closed vessels A B and C are at the same temperature T and contain gases which obey the Maxwellian distribution of velocities Vessel A contains only O B only N and C a mixture of equal quantities of O and N If the average speed of the O molecules in vessel A is V that of the N molecules in vessel B is V2 the average speed of the O molecules in vessel C is where M is the mass of an oxygen molecule 2 V 1 V V 2 TT 1 2 0 A OKTIM

17 A light container having a diatomic gas enclosed within is moving with velocity v Mass of the gas is M and number of moles is n The kinetic energy of gas w r t ground is MV 1 MV 3 nRT 2 5 3 MV nRT mass of gas M temperature T 2 MV 2 5

42 The ratio of de Broglie wavelength of molecules of hydrogen and helium gas moving at rms speed in two gas jars kept separately at temperature 27 C and 127 C respectively is b a c 2 3 3 4 d 2 1 38 V3

14 A diatomic ideal gas is heated at constant volume until the pressure is doubled and again heated at constant pressure until the volume is doubled The average molar heat capacity for the whole process is 2 1 3 13R 6 23R 6 4 19R 6 17R 6

The rms speed of hydrogen molecules at a certain temperature is 300m s If the temperature is doubled and hydrogen gas dissociates into atomic hydrogen the rms speed will become 1 100m s 2 300m s 3 600m s 4 300 2m s

An ideal gas with pressure P volume V and temperature T is expanded isothermally to a volume 2V and a final pressure P The same gas is expanded adiabatically to a volume 2V the final pressure is PA In terms of the ratio of the two specific heats for the gas y the ratio P PA is Question Type Single Correct Type 1 2Y 1 2 2 Y

A gas mixture consist of 3 0 mole of hydrogen and 2 0 mole of Helium at absolute temperature T Considering all vibrational modes assume zerc internal energy at T 0 the total internal energy of the system is 1 11 5 RT 3 13 5 RT 2 10 5 RT 4 15 0 RT 10 00

2 Figure shows the variation in internal energy U of 3 moles of Hydrogen gas with volume The work done by gas from state A to B is UA 2U U 1 In 2 5 and D V B C 2V V 2 3Ue In 2 5

Q14 Carbon dioxide contained in a piston cylinder device is compressed from 0 3 to 0 1 m3 During the process the pressure and volume are related by P aV where a 8 kPa m Calculate the work done on the carbon dioxide during this process

When an air bubble rises from the bottom of a deep lake to a point just below the wate surface the pressure of air inside the bubble A is greater than the pressure outside it B is less than the pressure outside it C increases as the bubble moves up D decreases as the bubble moves up

Internal energy of n moles of hydrogen at temperature Tis equal to the internal energy of n moles of helium at n temperature 2 T The value of ratio n modes in hydrogen 103 34 5 3 is neglect vibrational

122 REE OF FREEDOM MONOATOMIC DI POLYATOMIC GASES A gas mixture consists of 2 moles of O and 4 mo of Ar at temperature T Neglecting all vibratio modes the total internal energy of the system is a 15 RT b 9 RT c 11 RT d 4 RT

Consider the following two statements Statement A The average kinetic energy per degree of freedom per molecule at a given temperature increases as degrees of freedom increase Statement B The ratio of molar specific heat at constant pressure to that at constant volume increases as the atomicity increases The correct statement is O Only A O Only B Both A and B Neither A nor B

35 In equilibrium the velocity of molecules of a gas depends on its temperature as 3 u x T 4 u cc T0 1 u x T 2 u xc T of a molecule ner degree of fr

B Current through the inductor L C Potential difference across resistance R D Current through the resistance R During an experiment an ideal gas is found to obey a condition constant Pi P P pressure and p is the density of gas The gas is initially at temperature To pressur P and density d The gas expands such that density changes to d 2 Then A Pressure of gas changes to 2P B Temperature of gas changes to 2T C The curve of above process on P T graph is a parabola D The curve of above process on P T graph is a hyperbola

14 Consider the two insulating sheets with thermal resistance R and R as shown in figure The temperature 0 is a b 0102R1R2 0 02 R R c 01R 02R2 R R2 01 02 R R2 R R R R 01R2 02R1 TH R R tetanoo 16 baised ei muist R2 20 0

80 Two identical vessels A and B contain masses m and 2m of same gas The gases in the vessels are heated keeping their volumes constant and equal The temperature pressure curve for mass 2m makes angle a with T axis and that for mass m makes an angle with T axis then a tana tan B b tana 2 tan c tan 2 tan a d None of the Above

Q 31 A gas occupies a volume of 0 1 m at a temperature of 20 C and a pressure of 1 5 bar Find the final temperature of the gas if it is compressed to a pressure of 7 5 bar and occupies a volume of 0 04 m 313 C 413 C 513 C 613 C

If one mole of the polyatomic gas is having two vibrational modes and is the ratio of molar specific heats for polyatomic gas p then the value of B is Question Type Single Correct Type 1 2 3 1 02 1 2 1 25 1 35

occupies a volume of 0 1 m at a temperature of 20 C and a pressure of 1 5 bar Find the final temperature of the gas if it is compressed to a pressure of 7 5 bar and occupies a volume of 0 04 m 313 C 413 C 513 C 613 C

Q 33 A certain amount of an ideal gas is initially at a pressure p and temperature T First it undergoes a constant pressure process 1 2 such that T 3T 4 Then it undergoes a constant volume process 2 3 such that T3 T 2 The ratio of the final volume to the initial volume of the ideal gas is 1 5 0 25 0 75 1 0

If Co and C represent the rms speed of monoatomic gas molecules and the speed of sound in that gas then Co C Co C hr Co C

The pressure P versus volume V of an ideal gas varies as shown in the given figure Which of the following graph may represent the variation of pressure P with temperature T P 3 P T V 2 P L L 4 T P T

A vessel contains 14 gm 7 moles of hydrogen and 96 gm 9 moles of oxygen at STP Chemical reaction is induced by pasing electric spark in the vessel til neof the gases is consumed The temperature is berught back to it s starting value 273 K The pressure in the vessel is TE 14 MM 7 terension 96 31419 HIM Staten ti va 4 ta tega end Put we were fare adite at afte ht 273 A 0 1 atm B 0 2 atm C 0 3 atm D 0 4 atm Your Answer C m