Kinetic Theory of Gases Questions and Answers

45 A sealed container with negligible coefficient of volumetr expansion contains He gas When it is heated from 300 to 600 K the average KE of He atom will be a Halved b Unchanged c Doubled d Increased by factor 2

In van der Waals equation of state of the gas law the constant b is a measure of A intermolecular repulsions B intermolecular attraction C volume occupied by the molecules D intermolecular collisions per unit volume

One mole of monoatomic gas is involved in the cyclic process as shown in the PV graph Extension of the line segments 1 2 and 3 4 pass through the origin and the curves 1 4 and 2 3 are isotherms Find the ratio if 2 V V Par

alf that exerted equal to that en is half the that exerted C 11 A gas mixture contains 8 moles of oxygen and 2 moles of argon at room temperature T The total internal energy of the mixture is a 11 RT c 22 RT 12 Two cylinders contain ideal diatomic gas b 23 RT d 26 RT Ag

At 27 C the speed at which maximum number of molecules belongs is 10 m s then molecular weight of gas is R 25 3 J mol k Question Type Single Correct Type 1 2 100 kg mole 4 50 kg mole 3 25 kg mole 10 kg mole

0 One mole of a monatomic gas is involved in the cyclic process as shown in the PV graph Extension of the line segments 1 2 and 3 4 pass through the origin and the curves 4 1 and 2 3 are isotherms Find the ratio V3 if V2 V V 2 P2 P1 1 V V 1 3 V

A certain mass of oxygen treated like an ideal gas P in 10 Pa undergoes a cycle shown on P T diagram here The maximum volume of gas during the cycle is 16 litres Select the correct statement s Take R 25 3 J mol K A B C D The mass of gas is 15 36 gm The mass of gas is 30 72 gm The minimum volume of gas during cycle is 12 litres The minimum volume of gas during cycle is 8 litres 300 400 T in

An ideal gas is in a chamber with the volume fixed Initially the root mean square speed of the atoms is 500 m s and the pressure of the chamber is 1 00 atm The chamber is then heated by a flame for a short period of time After reaching equilibrium the pressure of the chamber is 1 63 atm What is the root mean square speed of the atoms in the equilibrium state 392 m s 815 m s 487 m s 592 m s 307 m s 638 m s

undergoes the reversible cycle ABCA shown in the p V diagram below where AB is an isotherm The molar heat capacities are Cp at constant pressure and Cv at constant volume The net heat added to the gas during the cycle is equal to P P2 C A V RThV2 V1 Ic Th O Cp Th Tc Cv Th Tc RTh In V2 V1 Cp Th Tc B V V

As shown schematically in the figure two vessels contain water solutions at temperature T o potassium permanganate KMnO4 of different concentrations n and n n n molecules pe unit volume with An n n n When they are connected by a tube of small length 1 anc cross sectional area S KMnO4 starts to diffuse from the left to the right vessel through the tube Consider the collection of molecules to behave as dilute ideal gases and the difference in their partia pressure in the two vessels causing the diffusion The speed v of the molecules is limited by the viscous force Bv on each molecule where is a constant Neglecting all terms of the order An which of the following is are correct kg is the Boltzmann constant ni 122 A the force causing the molecules to move across the tube is AnkBTS B force balance implies n Bvl AnkBT C total number of molecules going across the tube per see is 47 S D rate of molecules getting transferred through the tube does not change with time

Adiabatic Process Constant Q 12 The initial volume of 0 18 kg of certain gas was 0 15 m at a temperature of 15 C and a pressure of 1 bar After adiabatic compression to 0 056 m the pressure was found to be 4 bar Find i Gas constant ii Molecular mass of the gas iii Ratio of specific heats iv Two specific heats one at a constant pressure and other at a constant volume and v Change of internal energy

One mole of ideal gas follows a law according to that its pressure varies with volume as P b where a and b are positive constant The temperature of gas at volume V a is NCERT Pg 325 a b b a R ab R 2 abR ab 4 Th 14 R

At ordinary temperatures the molecules of an ideal gas have only translational and rotational kinetic energies At high temperatures they may also have vibrational energy As a result of this at higher temperatures molar specific heat capacity at constant volume Cy is a 5 N W N a N W NA 2 R for a diatomic gas 3 b R for a monoatomic gas 2 c R for a diatomic gas 3 d R for a monoatomic gas 2

29 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 rms speed will become a 424 26 m s c 600 m s b 300 m s d 150 m s

Equal moles of two gases A and B are kept in chambers which have same volume and temperature Find the ratio of mean free path of gas B to mean free path of gas A if van der Waals constant b of gas A is 8 times that of gas B A 1 1 B 2 1

ns Two ideal polyatomic gases at temperatures T and T are mixed so that there is no loss of energy If F and F m and m n and n be the degrees of freedom masses number of molecules of the first and second gas respectively the temperature of mixture of these two gases is 1 2 3 4 n T n T ny n MT n E T njF n F n E T T F F njFjT n F T n n

At the same temperature pressure and volume of two gases which of the following quantities is constant X C D The number of molecules Average kinetic energy Root mean square velocity Mean free path

The absolute temperature of a gas is determined A B C The average momentum of the molecule The velocity of sound in the gas The number of molecules in the gas The mean squaro volocity of

The velocity of three molecules are 2 km s 4 km s 6 km s Find 1 me velocity ii root mean square velocity Ans i mean square velocity V 18 66 km root mean square velocity V 4 319 km

1 What is the average kinetic energy of molecules of an ideal gas leaking freely through an orifice of a container which has N molecules at pressure P in volume V 3PV A 2N B C PV 2N 3PV N 2PV

The temperature T F of a room at time t minutes is given by the formula below T 65 9 25 t for 0 t 25 a Find the room s temperature when t 0 t 16 and t 25 b Find the room s average temperature for 0 st 25 a At 0 minutes the temperature is degrees Fahrenheit degrees Fahrenheit degrees Fahrenheit At 16 minutes the temperature is At 25 minutes the temperature is b The room s average temperature is degrees Fahrenheit

contains A spherical balloon of volume 4 00 10 cm helium at a pressure of 1 20 x 105 Pa How many moles energy of helium are in the balloon if the average kinetic of the helium atoms is 3 60 x 10 22 J a 3 32 mol c 4 12 mol b 2 16 mol d 2 8 mol

A massless piston which can move without friction closes a sample of helium in a vertical thermally insulated cylinder which is closed at its bottom and the cross section of which is A 2dm Above the piston there is a fixed stand to which an unstretched spring of spring constant 2000 N m is attached whose bottom end is at a distance of 2 dm from the piston when the volume of the gas is Vo 8dm The 105 Pa external pressure is po 9 g 10m S The gas confined in the cylinder is heated with an electric heating element 1dm 10 How much heat is supplied by the element till it reaches spring A zero B 600 J C 8000 J 1000I Po www Vo Vo D Id B A Id

A closed hollow insulated cylinder is filled with gas at 0 C and also contains an insulated piston of negligible weight and negligible thickness at the middle point The gas on one side of the piston is heated to 100 C If the piston moves 5 cm the length of the hollow cylinder is 1 13 65 cm 2 27 3 cm 3 38 6 cm 4 64 6 cm

CER 5 A and B are the two radioactive elements The mixture of these elements show a total activity of 1200 disintegrations minute The half life of A is 1 day and that of B is 2 days What will be the total activity after 4 days Given The initial number of atoms in A and B are equal a 200 dis min c 500 dis min b 250 dis min d 150 dis min

3 Three moles of an ideal gas are in a rigid cubical box with sides of length 0 170 m The ratio of the forces that the gas exerts on each of the six sides of the box when the gas temperature are 27 C and 127 C is

54 A container contains n moles of O gas temperature T Now a fraction of the ga dissociates adiabatically without any change in th internal energy The final temperature is 1 3 5T 5 x 5 T 2 T a 5 a 4 T

5 A given sample of an ideal gas occupies a volume niveV at a pressure P and absolute temperature T The mass of each molecule of the gas is m Which of the following gives the density of the gas NEET Phase 2 2016 1 P KT P essstoob 2 298 Pm KT nelenco anismo N en

The value of Y for hydrogen helium and another ideal diatomic gas X whose molecules are not rigid but have an additional vibrational mode are respectively equal to 7 5 9 5 3 7 5 7 7 G P C c b d S M N 579 3 5 7 5 7

20 Two non reactive monoatomic ideal gases have their atomic masses in the ratio 2 3 The ratio of their partial pressures when enclosed in a vessel kept at a constant temperature is 4 3 The ratio of their densities is 2013 Adv a 1 4 c 6 9 b 1 2 d 8 9

Inside a cylinder having insulating walls and closed at ends is a movable piston which divides the cylinder into two compartments On one side of the piston is a mass m of a gas and on the other side a mass 2 m of the same gas What fraction of volume of the cylinder will be occupied by the larger mass of the gas when the piston is in equilibrium Consider that the movable piston is conducting so that the temperature is the same throughout 1 2 1 4 4 1 3 3 1 20 20 3

4 0 g of a gas occupies 22 4 L at NTP The specific heat capacity of the gas at constant volume is 5 0 J K mol 1 If the speed of sound in this gas at NTP is 952 ms then the heat capacity at constant pressure is Take gas constant R 8 3 JK mol a 8 0 JK 1 mol 1 b 7 5 JK 1 mol 1 c 7 0 JK mol 1 d 8 5 JK 1mol 1 NEET 2015

c KE per unit volume d KE per unit mass 5 The average kinetic energy of the molecules of an ideal gas at 10 C has the value E The temperature at which the kinetic energy of the same gas becomes 2E is b 10 C d None of these a 5 C c 40 C 6 A polyatomic gas with n degrees of freedom has a mean energy per molecule given by

a twice c four times d one fourth In case of hydrogen and oxygen at NTP which of the following is the same for both a Average linear momentum per molecule b Average KE per molecule d KE per unit mass c KE per unit volume

In a thermodynamic process on an ideal monoatomic gas the infinitesimal heat absorbed by the gas is given by TAX where T is temperature of the system and AX is the infinitesimal change in a thermodynamic quantity X of the system For a mole of monatomic ideal gas V Here R is gas constant V is volume of gas T and VA are constants T X Rin R The List I below gives some quantities involved in a process and List Il gives some possible values of these quantities List I 1 Work done by the system in process 123 II Change in internal energy in process 1 2 3 III Heat absorbed by the system in process 1 2 3 IV Heat absorbed by the system in process 1 2 To To 3 Vo List II 1 P RT n2 2V 3 R RT S U T RT 3 n2 If the process is on one mole of monatomic ideal gas is as shown in the TV diagram with Povo RT the correct match is RTO 6 RTO

SolveLancer Test Same amount of heat is given to equal masses of a monoatomic and a diatomic gas The rise in temperature of monoatomic gas will be SolveLancer Test a Less than rise in temperature of diatomic b More than rise in temperature of diatomic c Same temperature rise in both d The rotational kinetic energy of diatomic gas will not change

A vessel contains a mixture of nitrogen of masss 7 g and carbon dioxide of mass 11 g at temperature 290 K and pressure 1 atm The density of the mixture is 1 1 1 g L 3 1 51 g L 2 1 2 g L 4 1 6 g L

9 An ideal mono atomic gas is trapped in a cylinder closed at its right end The cylinder is divided into two parts by a fixed heat conducting partition and a piston that is to the left of the fixed partition The piston and walls of the cylinder cannot conduct heat Masses of the gas in the left and right parts are m and m A force F applied on the piston is slowly increased starting from some initial value What is the molar specific heat of the gas in the left part during this process 3m R 3m R b a c 2m 3m R 2m d 2m 2 3m R 2m F

The ratio of number of collisions per second at the walls of containers by He and O gas molecules at at same volume and same temperature is assume normal incidence on walls 1 2 1 3 2 2 1 kept kept at 2 1 2 4 1 2 2

Question A gas at 30 C is heated at constant pressure till its volume is doubled Find the fina temperature of the gas 151 5 degree kelvin 0 0066 degree kelvin 606 degree kelvin 60 degree kelvin

An exhaust fan in a building should be able to move 2 5 kg s air at 98 kPa 20 C through a 0 4 m diameter vent hole How high a velocity must it generate and how much power is required to do

6 For a gas Cp 3 then gas may be R 1 Monatomic 2 Diatomic 3 Polyatomic 4 Mixture of monatomic and diatomic 5 Th be

Three moles of triatomic gas having linear molecular structure undergoes process given by 2 P 100 where V is the volume and P V is pressure Then change in internal energy of gas when volume changes from 1 m to 3 m is Ignore vibrational degrees of freedom O 200 J 300 J 500 J 600 J

8 One mole of a diatomic gas undergoes a thermodynamic process whose process equation is Pal The molar specific heat of the gas is 17R 17R 3 6 1 2 3 15R 4 4 15R 8

Very Short Answer VSA 1 MARK Each 1 Under which condition laws of Boyle Charles and Gay Lussac are valid 2 On what the values of absorption coefficient reflection coefficient and transmission coefficient depend in addition to the material of the object on which the radiation is incident

A gas mixture consists of 3 moles of nitrogen gas and 2 moles of neon gas at temperature T If vibrational mode is not taken into consideration then total internal energy of the system is 12RT 31 2 RT 17RT 21 DT

Two identical glass bulbs are interconnected by a thin glass tube at 0 C A gas is filled at N T P in these bulb is placed in ice and another bulb is placed in hot bath then the pressure of the gas becomes 1 5 times The temperature of hot bath will be 1 100 C 3 256 C Ice L Hot water 2 182 C 4 546 C

Two containers of equal volume contain same gas at pressure P and 3P respectively and temperatures 2T and T respectively On joining the vessels the gas reaches a common pressure Po and common Po temperature To The value of 7P 47 3P 4T 4P 7T 4P 3T is

The graph between pressure of an ideal gas and the root mean square speed of its molecules is Assume constant density Ellipse Parabola Hyperbola Straight Line

From the given graph which of the following conclusions can be drawn u is number of moles Ideal gas J mol pV HT 0 T T T3 200 400 600 800 p atm T T2 T3 T T2 T3 T T2 T3 T T T3