Kinetic Theory of Gases Questions and Answers

10 mol of an ideal gas y 1 5 behave as working substance in an engine working in a cycle as shown below 0 The process AB BC CD and DA are respectively reversible isobaric reversible adiabatic reversible isochoric and reversible isothermal The ratio of maximum to minimum temperature is 3 If maximum temperature is 600K Which is are correct statement s about BC process A Change in enthalpy is 12 kcal Change in internal energy is 8 kcal B D Change in entropy of gas is zero Work done on the gas is 8 kcal

An ideal monoatomic gas undergoes a process in 26 which the gas pressure relates to temperature as PT constant Then molar specific heat of gas in this process is 1 R 2 3 3R 2 2 R 4 7R 2 ve the form er fare 1 R 2 3 3R 2 PT Ferdin 2 R 4 7R 2 4

SolveLancer Test An ideal gas is heated from Ti to Tf in a closed vessel The difference between Tf and Ti is 5 C The pressure becomes times its initial value Calculate 21 20 Ti SolveLancer Test a 200 K b 100 K c 150 K d 300 K

Aar has a mixture of hydrogen and oxygen gases in the ratio 1 5 the ratio of mean kinetic energy of hydrogen and oxygen molecule is 1 1 16 3 1 5 2 1 4 4 1 1 looules of enclosed gas is v What will be the rms speed if pressure is doubled

A monatomic ideal gas expands from i to fas indicated in the P V diagram below If 8 5 MJ of heat are absorbed by the gas during the process if what is the final pressure P in MPa of the gas P Pa 0 1 2 4 V m

1 Two steady streams of air are mixed in a T junction as shown in the figure Stream one is at 32 C have a velocity and volumetric flow rate of 180 m min and 56 m min respectively Stream two is at 24 C flows with 120 m min in a duct diameter of 1 2m Mixed air flows with 150 m min Assume air behave as an ideal gas with Cp 1 kJ kgk Neglect potential and kinetic energy changes heat transfer and determine the mixed air temperature and the duct diameter of the mixed air section Outside air at LAVI Return air 7 24 C Dj 1 2 m

The energy radiated by a black body at 2300 K is found to have the maximum at a wavelength 1260 nm its emissive power being 8000 Wm 2 When the body is cooled to a temperature T K the emissive power is found t decrease to 500 Wm Find The wavelength in nm at which intensity of emission is maximum at the temperature T

Q No 5 Marks 4 00 2 00 View In English A certain amount of ideal gas expands along the straight line path ABC on P V diagram as shown in the figure The dotted curve represents the adiabatic for the same gas Along the straight line path P l A V

b The volume occupied by a gas at 300 K is 1 0 lit mole Compare the corresponding pressures considering the gas to be i ii An ideal gas A van der Waal s gas given a 1 32 atm lit mole 2 and b 0 312 lit mole 6

Two flasks of equal volume connected by a narrow tube of negligible volume contain 2 moles of H gas at 1 atm pressure and 300 K Now one of the flask is heated to 400 K and the other is maintained at 300 K What is the final pressure 8 1 atm 5 7 3 atm 5 2 4 5 3 8 7 atm atm

The number of molecules with energy range E is given by 3 2 TXT E1 2e E KT RKT n E 2nn Deduce the expressions for the following i The most probable energy ii The number of molecules containing the most probable energy 2 2

One mole of an ideal gas is taken through the cyclic process shown in the V T diagram where V volume and T absolute temperature of the gas Which of the following statements are correct heat is given out by the gas heat is absorbed by the gas the magnitude of the work done by the gas is RT In 2 the magnitude of the work done by the gas is VoTo V 2V0 A A Vo D To T C 2T

12 At constant pressure the ratio of increase in volume of an ideal gas per degree rise in kelvin temperature to its volume is Manipal 2015 a 1 T b 1 T c T d T 13 Water is heated from 0 C to 10 C then its volume

Estimate the time needed for blood hemoglobin to diffuse a distance of 5 m in water at 20 C Assume the diffusion constant is 6 9x10 11 m 2 s Select one O 18 1 ms 181 s O 181 ms

53 A vertical cylinder closed at both ends is fitted with a smooth piston dividing the volume into two parts each containing one mole of air At the equilibrium temperature of 320 K the upper and lower parts are in the ratio 4 1 The ratio will become 3 1 at a temperature of a 450 K c 420 K b 228 K d 570 K

4 The volume of an air bubble becomes two times as it rises from the bottom of a lake to its surface Assuming atmospheric times of 1 pressure 75 cm of Hg and the density of water is density of mercury The depth of the lake is 11 a 11 m b 5 6 m c 7 m d 6 8 m

Q 2 Ms Usha a science teacher performed the following experiments Experiment 1 She heated sugar in a China dish A black substance was obtained along with caramel fumes Experiment 2 She mixed sand and crushed naphthalene balls in a China dish Then she covered the China dish with a watch glass with some ice kept on it and heated Crystals of pure naphthalene were seen on the underside of the watch glass Identify the changes taking place in these experiments Select an option Clear Res Experiment 1 Chemical change Crystallisation Experiment 2 Physical change Decomposition Experiment 1 Physical chang lication

36 According to which law all perfect gases change in volume by 1 273th of their original volume at 0 C for every 1 C change in temperature when pressure remains constant a Joule s law b Boyle s law c Regnault s law d Gay Lussac law e Charles law

of 27 C Keeping pressure constant the volume would be doubled by raising the temperature to 1 54 C 3 270 C 4 540 C 2 327 C A flask is of a capacity one litre What volume of air will escape out from it on heating form 27 C t 7 C Assume pressure constant 1 033 L 2 33 3 mL 3 33 3 L 4 None of these

38 A ring shaped tube contains two ideal gases with equal masses and relative molar masses M 32 and 28 The gases are separated by one fixed M P and another movable stopper S which can freely without friction inside the ring The ea in equilibrium as shown in the figure in degrees is M move a 291 P M b 219 a S c 129 42 d 192

a c 273 C 7 A room temperature the rms speed of the molecules of certain diatomic gas is found to be 1930 ms The gas is a H 1930 b F c 0 d Cl tube contains two ideal gases with M 32 and

A quantity of monatomic ideal gas is taken from state a to state c along the path shown Va Vb 0 050 m3 and Vc 0 090 m3 Pa 1 0 X10 3 Pa and Pb Pc 2 0 X10 3 Pa How much work is done by the gas during this process A 20 J b 40 c 60 d 80 e 100

In an otto cycle air at 1 bar and 290 K is compressed isentropically until until the pressure is 15 bar The heat is added at constant volume until the pressure rises to 40 bar Take Cp 1 004 kJ kg k Cv 0 717 kJ Kg K

nal conductivities of the materials of s section as shown in the fig three rods of equal 5K K 2 the rods are K 2 5K and K respectively The end A and end B are at constant tem Heat entering face A goes out of the end B without any loss from the sides of the ba effective thermal conductivity of the bar A An adiabatic chamber has frictionless insulated piston of mass m Mass of the remaining chamber including gas is 4m n moles of an ideal monoatomic gas is present inside the chamber at atmospheric temperature and pressure Piston is in rest at equilibrium and confined to move along the length of the cylinder A particle of mass m moving horizontally with speed v strikes elastically with the piston Find the change in temperature of the gas when the compression of the gas is maximum m Im Workdor by K E

14 Consider a mixture of gas molecule of types A B and C having masses mA m mc The ratio of their root mean square speeds at normal temperature and pressure is a VA VB VC c VD 0 1 VA VB VC 1 1 b

mple Three moles of ideal gas A with C C 4 3 is mixed with two moles of another ideal gas B with C C 5 3 The C C of mixture is Assumin temperature is constant n 2 Y 5 3 3 2 Ymix A 1 5 B 1 42 C 1 7 D 1 3

The figure below shows n 4 moles of an ideal gas taken through a complete cycle A B C D A The gas is initially in state with pressure volume and temperature respectively of P V and T and it moves through the cycle with two isobaric and two isovolumetric processes Use the following as necessary P and V nP W P P a Determine the net work done on the gas per cycle b Determine the net energy added by heat to the system per cycle

e have a sample of gas characterised by P V and T and another sample of 2P V 4 and 2T What is the ratio of the number of molecules in mples 2 1 B 16 1 C 8 1 gas characterized first and second osalli

When material falls from the cloud to the star potential energy is first converted to kinetic energy and then to heat The potential energy of a particle with mass m in the potential of a mass the star M at a distance Ris U grav m GMm R If a particle falls down infinitely far from on a solar mass star with a radius of 4 R sun and all the energy is converted into heat what temperature does it get you can assume that the particle is one hydrogen molecule

13 A gas mixture consists of 2 moles of oxygen and 13 4 moles of argon at temperature T Neglecting all vibrational modes the total internal energy of the system is 1 4 RT 3 9 RT 2 15 RT 4 11 RT att 1 4RT 3 9 RT 2 15 RT 4 11 RT 3

16 4 0 g of a gas occupies 22 4 litres at NTP The specific heat capacity of the gas at constant volume is 5 0 J K mol If the speed of sound in this gas at NTP is 952 m s then the heat capacity at constant pressure is Take gas constant R 8 3 J K mol a 7 0 J K mol b 8 5J K mol 1 d 7 5 J K mol 1 1 c 8 0 J K mol 2015

Temperature of a diatomic gas is 300 K If moment of inertia of its molecules is 8 28 x 10 38 gm cm root mean square angular velocity is A B D 1012 rad s 10 108 rad s 1 5 10 2 rad s 15 108 rad s

The speed of sound in oxygen O at a certain temperature is 460 ms 1 The speed of sound in helium He at the same temperature will be assume both gases to be ideal A B C 650 ms 1 330 ms 1 460 ms 1

GREEMEN The viscosity of a gas depends on mass the effective diameter and the mean speed of the molecules At room temperature for He He 2 x 10 5 kgm 8 and for CH4 CH 1 1 10 5kgm s The diameter of the He atom is 2 1 x 10 10m If the diameter of CH4 is n x 10 0m find n Given mean speed of the molecules of the gas v x where KB is the boltzmann s constant Tis temperature and m is the mass of the gas 2 1 KBT 3 2

If the gas in a confined container constant volume were to have its temperature raised from 55 degrees C to 160 degrees C what would the final gage pressure be if the initial pressure were 220 psig Note Temperature and pressure must be converted to their absolute values This is a direct proportion C 273 K PSIG 14 7 PSIA O O 295 13 psig 309 83 psig ALL

Which of the following situations would cause the greatest decrease in the motion of molecules in a system OA Q 50 J W 50 J OB Q 50 J W 50 J OC Q 50 J W 50 J OD Q 50 J W 50 J

On a hot summer day the temperature of air in Arizona reaches 102 F What is the speed of sound in air at this temperature The speed of sound at 0 C is 331 m s Use the conversion 0 C 273 K as necessary m s Nood Help F Dend

Q 124 Certain amount of dry air at N T P is Q 124 NTP ten er en gud compressed to th of its original volume 4 suddenly If y 1 5 the final pressure would be 1 4 atm 2 6 atm 3 8 atm 4 16 atm fy 1 5 1 4 atm 3 8 atm th 4 the full vid 2 6 atm 4 16 atm

Heat is associated with 1 kinetic energy of random motion of molecules 2 kinetic energy of orderly motion of molecules 3 total kinetic energy of random and orderly motion molecules 4 kinetic energy of random motion in some cases an kinetic energy of orderly motion in other

44 If two moles of an ideal monatomic gas at temperature To are mixed with 4 moles of an ideal diatomic gas at temperature 270 then the temperature of the mixture is 0 1 9 5 23 To To 2 17 To 13 13 4 To

Flask A of volume 10 liter containing 20 gram of H and flask B of volume 10 litre containing 88 gram CO are connected by a connector having negligible volume When valve of the connector is opened what is the composition of H gas in flask B after openening the valve 20 g 10 Litre Thermo state at 500 K 1 10 2 13 3 15 4 20 88 g CO 10 Litre Thermo state at 200 K

One mole of an ideal monoatomic gas is taken round the cyclic process ABCA as shown in fig cal P a b c 3P P B C sochore The work done by the gas Volo The heat rejected by the gas in the path CA and heat absorbed in the path AB B AC OT The net heat absorbed by the gas in the path BC Q AGAT

One mole of an ideal monoatomic gas y 5313 is mixed with one 7 5 mole of a diatomic gas heat at constant pressure to that at constant volume find y for the mixture y denotes the ratio of specific

The number of molecules in one litre of gas 25 at temperature 27 C and pressure of 106 dyne cm 2 is 1 2 4 x 1021 3 3 2 1021 2 2 4 x 1020 4 2 4 x 1022

In an isobaric process of a monoatomic gas 100 J of heat is added to n moles of the gas to increase temperature from T to T The amount of work done by the gas in the process is 1 20 J 2 30 J 3 60 J 4 40 J S S 70 08

Please refer to this picture already present in doubt count er From this I have a confusion that 3 2kt is given for all g ases irrespective of the nature But for diatomic gas say fo r example is it 5 2kt then If we consider degree of freedo m If yes then how can we say that for all type of gases it i s 3 2kt Doesn t average KE differ from molecule to molecule based on whether molecule is monoatomic diatomic or polyatomic Because degrees of freedom differ ats Kinetic Interpretation of Temperature Average kinetic energy per molecule of a gas is 3 M kgT 2 Average kinetic energy per molecule of a gas depends on on its absolute temperature It is independent of press volume and nature of the ideal gas At a given temperature the average kinetic energy p molecule of all the gases are same Ra

AU 35 An ideal monoatomic gas undergoes a process in its internal energy U and density p vary as Up constant The ratio of change in internal energy 2 MCWon which 2C vand the work done by the gas is 379 2 b 3 a 2 c 3 d 3 5

Sound waves travel from a location A at absolute temperature T to location Bat absolute temperature T2 in a time t The air temperature increases linearly from T to T If speed of sound in air varies with absolute temperature T as v k T where k is a positive constant Then eqfa a d 1 999 929 319 7 92 KA A 439 2 Ba ha m m 7 1 ch tuu a a 21 uk ay eaf A v T Rafa si kyh uachg Audih 21 ac A Distance between A and B is kt 2 B is T T 2 D 2k 3 Correct Answer kt 2 T T The average velocity over the interval t 3 2 T3 T3 T2 T1 a 2k 3 C The average velocity over the interval t k T T V is 2 kt T T T3 T3 2 T2 T1 Correct Answer k T1 Tz 2 2 The distance between A and B is

An electron accelerated application magnitude E The magnitude of the rate of change of its de Broglie wavelength at time t is given by A B C D h eE h eEt h eEt mh eft of mass m and charge e is from rest at time t 0 by of a constant electric field of

In the following figure A certain mass of gas traces three paths 1 2 and 3 from state A to state B If the work done by the gas along these paths are W W2 and W3 respectively Then A W1 W2 W3 C W1 W2 W3 3 B W1 W2 W3 D W W2 but W3 W2