Kinetic Theory of Gases Questions and Answers

O One kg of a diatomic gas is at pressure of 8 104 N m The density of the gas is 4 kg m The energy of the gas due to its thermal motion will be 1 3 104 J 2 5 x 104 J 3 6 104 J 4 7 104 J

Two closed containers of equal volume filled with air at pressure Po and temperature T Both are connected by a narrow tube If one of the container is maintained at temperature T and other at temperature T then new pressure in the containers will be 2P T 1 T To POT 3 2 T To PT 2 T To 4 T To Po

An ideal gas is filled in a closed container and container is moving with uniform acceleration in horizontal direction Neglect gravity Pressure inside the container is 1 Uniform everywhere 2 Less in front 3 Less at back 4 Less at top

An ideal gas undergoes a polytropic given by equation PV constant If molar heat capacity of gas during this process is arithmetic mean of its molar heat capacity at constant pressure and constant volume then value of n is 1 Zero 3 1 2 1 4 X

The temperature 7 of one mole of an ideal gas varies with its volume V as T V BV where a and are positive constants The maximum pressure of gas during this process is 1 3 a 2R a B R 282 2 4 B R 4 a R 28

2 If one mole of the polyatomic gas is having tw vibrational modes and is the ratio of mola Cp B C the specific heats for polyatomic the value of is 1 1 02 3 1 25 Official Ans by NTA 2 Sol 2 f 4 3 3 10 assuming non linear C 2 B 14 1 f 12 10 2 1 2 4 1 35 gas 1 2

Consider the following two statements a If a gas container in motion is suddenly stopped th temperature of the gas rises b A gas can be liquefied at any temperature by increase of pressure alone The correct statement s is are a only b only Both a and b Neither a nor b

The graph between the mean free path and the radius of molecules for a given number density is Linear Hyperbola Parabola Ellipse

The expansion of unit mass of a perfect gas at constant pressure is shown in the diagram Here a K Question Type Single Correct Type 1 2 3 a volume b C temperature a volume b K temperature a C temperature b volume 4 a K temperature b volume

square rms velocity to the average velocity of gas molecule would be Molecular weight of oxygen is 32 g mol R 8 3 J K mol 100100001 8T V 3 3 V8 Question Type MCC Question ID 8643

ree ideal gases H CH4 and SO2 are filled in three rigid containers A B and C respectively WH 64 gm W 64 CH V 2L T 200 K gm V 1 L T 400 K WSO 128 gm V 2L T 1600 K A B C X the simplest ratio of most probable speeds of gases in respective containers is X Y Z then calculate the value of 7

A horizontal tube of length closed at both ends contain an ideal gas of molecular mass M The tube is rotated with angular velocity w about a vertical axis passing through an end If temperature is constant and P P2 are pressures at free end and fixed end respectively then 1 P P 2 P P P 3 P P 4 P

6 If one mole of the polyatomic gas is having two vibrational modes and is the ratio of molar specific heats for polyatomic gas B ons 1 1 02 2 1 2 3 1 35 4 1 25 Cv then the value of is

1 In a constant volume gas thermometer the pressure of the gas in the bulb is 28 cm and 44 cm of Hg at temperature 0 C and 100 C respectively Pressure of the bulb at temperature 50 C will be 1 32 cm of Hg 2 34 cm of Hg 3 36 cm of Hg 4 38 cm of Ha X8 168m

The root mean square rms speed of hydrogen molecules at a certain temperature is 300 m s If the temperature is doubled and hydrogen gas dissociates into atomic hydrogen the r m s speed will become 1 424 26 m s 2 300 m s 3 600 m s 4 150 m s

Illustration 17 At what temperature does the average translational kinetic energy of a molecule in a gas equal to the kinetic energy of an electron accelerated from rest through a potential difference of 5 volt

2 Illustration 19 Two perfect gases at absolute temperatures T and T are mixed There is no loss of energy If masses of the molecules are m and m and number of molecules in the gases are n and n the temperature of mixture will be

Illustration 8 A closed container of volume 0 02 m contains a mixture of neon and organ gases at a temperature of 27 C and pressue of 1 x 105 N m The total mass of the mixture is 28 gm If the gram molecular weight of neon and organ are 20 and 40 respectively then the masses of neon and argon in the mixture will be respectively

Two bulbs A and B of same volume contain an ideal gas at temperature T and pressure p When the temperature of the bulb B is doubled and that of A remains unchanged the pressure of the gas will be Neglect the volume of the tube connecting the two bulbs 1 2p B 1 5p A 2 4 1 2p B

1 At 27 C temperature the kinetic energy of an ideal gas is E If the temperature is increased to 327 C then kinetic energy would be 1 2E 2 E 2 3 ZE

A sample of an ideal gas has pressure Po volume Vo and temperature To It is isothermally expanded to twice its original volume It is then compressed at constant pressure to have the original volume Vo Finally the gas is heated at constant volume to get the original temperature The heat absorbed in the process is a Polo In 2 PV In 2 c polo ln 2 21 2Vot Vot a x n d To 3 b PoVo In 2 In 2 1 T

5 Average velocity of oxygen molecules at 27 C in a container at rest is 1 980 m s 3 370 m s 2 Zero 4 863 m s

1 A flask contains neon and oxygen in the ratic 4 5 by mass The temperature of the mixture is 50 C The ratio of their mean translational kinetic energy is assume ideal gas behaviour 1 1 1 2 2 5 3 4 5 1 16

Illustration 12 The velocities of four molecules of a gas are 3 3 4 6 m s the root mean square velocity will be

Illustration 13 The temperature of an ideal gas increased from 120 K to 480 K The root mean square velocity of the gas molecules is v at 480 K it becomes

9 The rms velocity of nitrogen molecule in a cylinder containing nitrogen gas at 17 C is 5x10 2 m s If the diameter of the nitrogen molecule is roughly 2 0A and no of molecules per unit volume is 2 56x10 25 then the time taken for the collision between two nitrogen molecules 1 2 10 1 S 3 3x10 13S 2 4 4x10 20S 4 1 10 1 S 3999

The temperature of n moles of an ideal gas is increased from T to 27 through a process P 0 1aT The work done by the gas is given by a is constant and P is initial pressure 1 2anR Po 2 Zero

A vessel contains a mixture of one mole of oxygen and two moles of nitrogen at 300 K The ratio of the average rotational kinetic energy per O molecule to that per N molecule is A 1 1 B 1 2 C 2 1 D depends on the moments of inertia of the two molecules 1998

5 The given graph represent the variations compressibility factor Z versus p for three real pV nRT gases A B and C Identify the only incorrect statement 2006 5M nive explanation 1 Z C A B A Ideal gas B C 0 p atm a For the gas A a 0 and its dependence on p is linear at all pressure b For the gas B b 0 and its dependence on p is linear at all pressure c For the gas C which is typical real gas for which neither a nor b 0 By knowing the minima and the point of intersection with Z 1 a and b can be calculated d At high pressure the slope is positive for all real gases

Two thermally insulated vessels 1 and 2 are filled with air at temperatures T T volume V V and pressure P P2 respectively If the valve joining two vessels is opened the temperature inside the vessel at equilibrium will be 2004 1 T T 3 T T P V P V P V T P V T 2 T T 2 4 T T P V P V P V T P T T

Three moles of an ideal monoatomic gas performs a cyclic process as shown in the figure The temperatures in different states are T 400K T2 800K T3 2400K and T4 1200K Determine the work done by the gas during the cycle Given R 8 31 J mole K p 1 2 a 19 94 kl h 22 65 kl 3 T c 15 81 kl d 10 37 kl

1 The volume of some amount of oxygen at 27 C and at 70 cmHg pressure is 400 cm What will be its volume at STP What change will be observed in the product of pressure and volume of the gas during this change 335 3 cm 2517 erg

4 At STP the density of air is 0 00129 g cm If the barometric height decreases from 76 cm to 74 cm then what will be the difference in the masses of 15 L of

3 15 RT 4 9 RT of the system is 1 11 RT 2 4 RT 15 An insulated container contains 4 moles of an ideal diatomic gas at temperature T Heat Q is supplied to this gas due to which 2 moles of the gas are dissociated into atoms but temperature of the gas remains constant The work done by the gas is 2 Q RT 4 Q 4 RT 1 Q 2 RT 3 Q 3 RT Jogule is 3 32 x 10

22 Calculate the mass of 1 litre of moist air at 27 C when the barometer reads 753 6 mm of mercury and the dew point is 16 1 C Saturation vapour pressure of water at 16 1 C 13 6 mm of mercury density of air at STP 0 001293 g cc density of saturated water vapour at STP 0 000808 g cc

because of their high speeds and incessant collisions In slight increase in density at lower heights like in the atmosphere The effect is small since the potential energy mgh for ordinary heights is much less than the average kinetic energy 2 mu of the molecules is not always equal to u 2 The average of a squared quantity is not necessarily the square of the average Can you find examples for this statement n Td vst 1 NTT lonular volume to the actual volume occupied by oxyg EXERCISES

The pressure of a gas ta 100 C is 2 atm When the gas is heated by keeping volume constant at what temperature the pressure raises to 3 atm 1 286 5 C 3 186 5 C 2 168 5 C 4 366 5 C

Two vessels A and B having equal volume contain equal masses of hydrogen in A and helium in B at 300 K Then mark the correct statement 1 The pressure exerted by hydrogen is half that exerted by helium 2 The pressure exerted by hydrogen is equal to that exerted by helium 3 Average KE of the molecules of hydrogen is half the average KE of the molecules of helium 4 The pressure exerted by hydrogen is twice that exerted by helium

2 A flask is filled with 13g of an ideal gas at 27 C and its temperature is raised to 52 C The mass of the gas that has to be released to maintain the pressure constant is 2000 E 1 5gm 2 6 gm 3 7 gm 4 1 gm

8 A vessel contains 8gm of a gas at a pressure P and temperature 500K The gas leaves through a small hole The mass of the gas leaked out when the pressure is P 2 and temperature is 400K is 1 5 gm 2 3 gm 3 4 gm 4 6 gm

Molecular heory Two thermally insulated vessels 1 and 2 are filled with air at temperatures T T volume V V and pressure P P respectively If the valve joining the two vessels is opened the temperature inside the vessel at equilibrium will be 1 T T 3 T T P V P V P V T2 P V T 2 4 T T 2 T T P V P V 2 P V T P V T

The kinetic energy of translation of 20 gram of oxyg 47 C is Molecular weight of O 32 gram mo R 8 3 J mol K a 2490 ergs c 249 J b d 2490 J 960 J 70

4 moles of diatomic ideal gas are heated at constant pressure from 27 C to 327 C The heat 2 cal mole K supplied to the gas is 1 3000 calorie 3 8000 calorie R 2 6000 calorie 4 8400 calorie

Which of the following is not an assumption of the kinetic theory of gases 1 A A gas consists of many identical particles which are in continual motion 2 3 4 Gas particles have negligible volume At high pressure gas particles are difficult to compress Collisions of gas particles are perfectly elastic

The average kinetic energy of a helium atom at 30 C is MP PMT 2004 a Less than 1 eV c 50 60 eV b A few keV d 13 6 eV

1 A vessel of volume 0 04 m contains a mixture of hydrogen and helium at 20 C and 2 atmospheric pressure and the mass of mixture is 10 g Then the ratio of mass of hydrogen to that of helium in the mixture is nearly 1 atm 105 Pa llow slovo 2 1 2 4 3 2 1 1 3 3 2 3

154 The mean free path for a gas with molecular diameter d and number density n can be expressed as 1 3 4 1 2 n d 1 2 nnd 1 2 n nd 1 5 22 2 h nd

1 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 T A good estimate for q is 1 2 2 3 4 1 1 2 1

I A fix amount of nitrogen gas subjected to pressure and temperature variation The experiment is performed at high pressure as well as high temperatures The results obtained are shown in the figures The correct variation of PV RT with P will be exhibited by UPSEAT 2001 201 4 PV RT a 4 1 0 3 100 200 400 b 3 2 600 1 P

7 The amount of heat energy required to raise the temperature of 1 g of Helium at NTP from T K to T K is 1 NakB T T 3 2 N KB T T 4 3 3 NakB 4 3 ALK T T