Kinetic Theory of Gases Questions and Answers

The figure shows the plot of M 1 T T 3 T T PV vs P for oxygen gas at two different temperatures then nT PV nT 2 P more corved le 2 T T 1 4 May be 1 2 Otroch Tower 8 Pusa Road New Delhi 110005 PH

3 3 4 6 23 If a gas has degree of freedom the ratio of the specific heats of the gases 1 3 1 f 2 C C 2

A box of negligible mass containing 2 moles of an ideal gas of molar mass M and adiabatic exponent y moves with constant speed v on a smooth horizontal surface If the box suddenly stops then change in temperature of gas will be 1 Y 1 MV 4R Mv 3 2 Y 1 R 2 4 YMv 2R Y 1 Mv 2R 5

26 E and E respectively represents the average kinetic energy of a molecule of oxygen and hydrogen If the two gases are at the same temperature which of the following statement is true 1 Eo EH 3 Eo E 2 E E 4 Data insufficient

The point group symmetrics of the three molecules shown in Figs 1 3 are respectivel temperature is linear with an intercept Tc H CI CI CI H H Fig 1 notation Cay 2mm a C h C v C h c D C C 1 TL H Fig 2 C2h 2 m H CI H Fig 3 D2h mmm b C C C h 8 C

A sample of gas in a box is at pressure P and temperature To If number of molecules is doubled and total kinetic energy of the gas is kept constant then final temperature and pressure will be 1 To Po 2 T 2P 2 2 12 13

In an isothermal process two moles of an ideal gas expands from volume 2 m to 8 m at temperature of 227 C Heat absorbed by the gas during process is nearly 1 2752 cal 3 1945 cal NCERT Pg 311 1 2 3250 cal 4 1875 cal

9 An ideal gas is compressed to half of its initial volume by means of different thermodynamic processes Which of the process result in the maximum work done on the gas NCERT Pg 312 1 Isothermal 2 Adiabatic 3 Isobaric Isochoric 2

A metal sheet with a circular hole is heated The hole 1 Gets larger 2 Gets smaller 3 Remains of the same size 4 Gets deformed EXERCISE stant volume gas thermometer shows pressure reading of 50 cm and 90 cm of mercury at 0 C and 100 ctively When the pressure reading is 60 cm of mercury the temperature is 5 C 2 40 C 5 C 4 12 5 C

A steel tank contain 300g of ammonia gas at pressure 1 35 106 Pa and temperature 77 C If some gas is removed from tank and temperature reduced to 27 C then pressure is 8 7 105 Pa Then find amount of gas leaked A B C 225 56 g 74 44 gm 200 g 70 Correct Answer

Van Der Waals Equation 10 moles of CO gas is taken from an INITIAL STATE 300K 0 1 m to a FINAL STATE 300K 0 2 m Van Der Waals equation is P an V nb nRT m6 mol m mol Where a 0 3643 Pa R 8 314 J mol K and b 4 27 x 10 5 for CO Gas 6 Find the Pressure in the INITIAL STATE denoted by Pia using ideal gas equation 7 Find the Pressure in the INITIAL STATE denoted by Pod Jusing Van Der Waals equation of state 8 Find the value of of relative error in the INITIAL STATE using the formula e pl 11 Find the value of relative error in the FINAL STATE using the formula ef 12 Why is ef less than e vd 9 Find the Pressure in the FINAL STATE denoted by Pi using ideal gas equation 10 Find the Pressure in the FINAL STATE denoted by PJusing Van Der Waals equation of state id id

N molecules each of mass m of gas A and 2N molecules each of mass 2m of gas B are contained in the same vessel at temperature T The mean square of the velocity of molecules of gas B is velocity of molecules of gas A is and the mean square of x component of the 2 The ratio 1 1 3 2 2 is 4

0 Identical balloons are connected through identical valves with two identical cylinders One cylinder contains gaseous helium and the other gaseous nitrogen Both the gases may be assumed ideal and both the cylinders weigh equally Which balloon will be inflated faster when the valves are opened and why a The nitrogen balloon will be inflated faster because nitrogen is a heavier element and so the molecules of nitrogen have greater momentum and thus force the balloon to expand at a greater rate b The helium balloon will be inflated faster because helium is a lighter element and so its atoms move faster and can get into the balloon at a greater rate c The helium balloon will be inflated faster because the helium must be at higher pressure and hence the gas will be forced into the balloon at a greater rate d It will depend on whether the gases have to flow up or down to enter the balloon Helium being lighter than air as compared to nitrogen will rise faster than nitrogen Therefore if the balloons are at the top of the cylinders the helium balloon will be inflated faster and if they are at the bottoms the nitrogen balloon will be inflated faster

4 None of the above A piston is slowly pushed into a metal cylinder isothermally containing an ideal gas them incorrect statement is 1 Pressure of the gas increases 2 Average speed of the gas molecules increases 3 The number of molecules per unit volume increases 4 None of these

Pressure of an ideal gas is increased by keeping 11 temperature constant What is its effect on kinetic energy of molecules 1 Increases 2 Decreases 3 No change 4 Cannot be determined cylinder containing an ideal gas has a piston 12 a fed ved 1 2 3 4 Uch fucuc UCH B della MECHEN fare

Speed of sound in air at room temperat approximately 343 m s What can be the of sound in Hydrogen at room tempe approximately 1 1284 m s 3 686 m s 2 2089 m s 4 440 m s

26 A mono atomic gas is filled in a heat insulated horizontal cylindrical is The P container at pressure p and temperature T Density of the gas container is abruptly made to move along its axis with a constant velocity u Find temperature of the gas when a new steady state will establish in the container in gaseous state under a light

120 A metal jar has a gas of volume 10 3m at a pressure of 2 x 10 Pa and temperature 400K The jar has small hole and hence the gas leaks into atmosphere The pressure and temperature of atmosphere is 10 Pa and 300K respectively If R is the gas constant the number of moles of the gas that has leaked into atmosphere is 10 m 3035055 2 x 10 Pa bas son 550 88 Ke 35 og Dado leak sob J n n dos b s Sobox 50x 300K Reb o ra grosin se redn 3600 L he 1 1 1 SR 2 6R od 400K e g duider 38 s 10 Pa D van n

A mixture of 2 moles of helium gas atomic mass 4 amu and 1 mole of argon gas atomic mass 40 amu is kept at 300 K in a container The ratio of the Vrms helium rms speeds Vrms argon is Question Type Single Correct Type 1 2 3 0 32 0 45 2 24

o Negative Marks 1 If wrong option is selected A vessel with open mouth contains air at 60 C When the vessel is heated upto temperature T one fourth of the air goes out The value of Tis O 80 C 171 C 333 C

A flask contains argon and chlorine in the ratio 2 1 by mass at a temperature of 27 C The ratio of molar mass of chlorine to argon is roughly 3 5 The ratio of average translational kinetic energy of argon to chlorine molecule is Options 1 75 7 1 1 41

Relation between the ratio of specific heats y of gas and degree of freedom f will be Question Type Single Correct Type 1 y f 2 2 1 1 1 A 11 NI 3 f 2 Y 1 f 2 x 1

Sri Chaitanya IIT Academy 20 12 15 Sr IPLCO Jee Adv 2011 P2 Q Paper 40 An ideal gas undergoes a reversible cyclic process according to the graph P is pressure V is volume W is work done by the gas AU is change in internal energy of the gas and Q is heat given to the system of gas Column I A For process AB B For process BC C For process CD D For process DA P V V Column II P AU 0 Q 0 Q AU 0 Q 0 R QXAUXW 0 S QXAU 0

What will be the average value of energy along one degree of freedom for an ideal gas in thermal equilibrium at a temperature T k is Boltzmann constant 1 KBT 2 KBT 3 KBT 4 KBT

Which of the following is always true for an ideal gas that goes through an isothermal process No work is done on or by the gas The internal energy of the gas does not change The entropy of the gas does not change There is no heat transfer into or out of the gas

Question No 18 If root mean square speed of hydrogen molecules at 300 K is 1930 m s then at 900 K evaluate the root mean square speed of oxygen molecules 1930 3 643 m s 1930 3 m s 836 m s m s W

The temperature reduces as the height incre ases Therefore the density in the higher ho rizons of the atmosphere might be more tha n the lower ones But it is not so because of gravity But why the assumption I made is w rong

Gas Pressure variation with height An ideal gas of molar mass M is located in uniform gravitational field in whi the free fall acceleration is g Find gas pressure as a function of height if gas temperature varies with height T T 1 ah At h 0 take pressure of gas be Po

vector of the object is A 31 4 12k B 3i 4j 12k C 31 4j 12k A particle goes along a quadrant of a circle of radius 10m from A to B as shown in f the magnitude of displacement and distance along the path AB is 08 0A OA B 8 OB OA A D 19mm

15 A uniform rope of length L and mass m hangs vertically from a rigid support A block of mass m is attached to the free end of the rope A transverse pulse of wavelength 2 is produced at the lower end of the rope The wavelength of the pulse when it reaches the top of the rope is 2 The ratio is m m a b m c m Vm m Vm d m m m NEET I 2016 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 5 J K mol d 7 5 J K mol c 8 0 J K mol 2015

A point moves with retardation along a circle of radius R so that at any moment Ram and Shyam are walking on two perpendicular tracks with speeds 3m s and 4m s respectively At a certain moment say t 0s Ram and Shyam at 40m and 20m away from the intersection tracks respectively and moving towards the intersection of the tracks A Shortest distance between them subsequently is 15m B Shortest distance between them subsequently is 20m C The time when they are at shortest distance from each other is 8s D The time when they are at shortest distance from each other is 9s

Two spherical vessel of equal volume are connected by a n arrow tube The apparatus contains an ideal gas at one atmosphere and 300 K Now if one vessel is immersed in a bath of constant temperature 600K and the other in a bath of constant temperature 300 K Then the common pressure will be conservo et mall

h a massive metal cylinder of height h 1 m closed on top by a moving piston is an ideal gas On top of the piston we gently put weight The piston immediately dropped by x 2 5 cm over a long time it was seen that the piston comes down another x 1cm Determine the degree of freedom for the molecules of the gas Room temperature is constant gas does not leak out Use binomial approximation

An incompressible non viscous fluid is injected into a conical pipe at its orifice as schematically shown in the figure The pressure at the orifice of area A is P Neglecting the effect of gravity and assuming streamline flow which one of the following plots correctly predicts the pressure along axis of the cone Options PA Xo Por Vo P Xo PA XP Xo PA Po Xo P Po Xo R 4 V oc Solution Answer A AV Constant A x x

Water is filled to a height of 18 0 m deep in a storage tank whose top is open to the atmosphere What are the absolute pressure at the bottom of the tank Use Acceleration due to gravity 9 8 m s Density of Water pwater 1000 kg m Atmospheric Pressure Patm 1 01 X10 Pa Select one a 2 77 x 10 Pa b 1 76 x 10 Pa 5 c 2 19 x 10 Pa

An ideal gas is contained in a 3 5 L container at a temperature of 28 C If pressure is k constant what is the final volume of the gas if the temperature of the container is increased to 245 C Select one a 27 L b 7 2 L c 6 L

External Work in displacing a Piston A piston can freely move inside a horizontal cylinder closed from both ends Initially the piston separates the inside space of cylinder in two equal parts each of volume V which are filled with an ideal gas at same pressure Po If temperature of gas in two parts is equal and kept constant find the work required to be done in increasing the volume of one part of gas n times compared to the other part by slowly displacing the piston

A Floating Cylinder in Water A thin walled cylinder of mass m height h cross sectional area S is filled with a gas and floats with a part of cylinder in water As a result of the leakage of water from the bottom of cylinder the depth of submerged part has increased by Ah Calculate the initial pressure of gas in cylinder Take atmospheric pressure Po and constant temperature

SolveLancer Test Density of diatomic gas is 0 800 kgm at temperature 400 K and pressure 4 atm Find the specific heat of the gas at constant volume SolveLancer Test a 2 125 x 104 J kg K b 1 25 x 104 Jkg K c 1 125 x 104 Jkg K 1 d 3 125 x 104 Jkg K

66 If the pressure of a gas is doubled at constant temperature then the mean square velocity will become 1 No change 3 Four times 2 double 4 None of the above

Illustrations 13 Molar Heat capacity of a Gas in Tuna Process Molar Heat Capacity of a Gas in Tuna Process One mole of an ideal gas having adiabatic exponent y undergoes the Tuna process in which gas temperature varies with volume according to function T Tev Find the molar heat

i A body cools from a temperature 3T to 2T in 10 minutes The room temperature is T Assume that Newton s law of cooling is applicable The temperature of the body a the end of next 10 minutes will be d T ST 2 a TT 4 c T 4 3

To what temperature should the hydrogen at room temperature 27 C be heated at constant pressure so that the R M S velocity of its molecules becomes double of its previous value 27 C 4 assiva s faud Gia 42 fad d 4 42 44 full fch 3 EICT 37TR ESIch HIV T N T 1 1200 C 2 927 C 3 600 C 397 4 108 C

Physics Question No 45 I II 8cm 8cm Question Palette In figure l an air column of length is entrapped by a column of Hg of length 8 cm In figure Il length amo air column at the samo tomperaturo is l

We have a sample of gas characterised by P V and T and another sample of gas characterised by 2P V 4 and 2T What is the ratio of the number of molecules in the first and second samples A B C 2 1 4 1 8 1

The average speed of 0 1 mol of gas A at 300 K was 460 m s The average speed of 0 2 mol of another gas B at 400 K was 510 m s The above two samples were mixed without any transfer of energy with the surrounding Calculate the average speed of gas mixture Assume gases A and B do not react

A solid sphere made of material of bulk modulus 2 x 10 N m is surrounded by a liquid in a cylindrical container A massless piston of area 1m floats on the surface of the liquid when a mass 6 kg is placed on the piston to compress the liquid then fractional change in the radius of the sphere is given by x x 10 7 then find x

An ideal gas is held in a non insulated rigid container with a volume of 20 L More gas is pumped into the container but the volume of the container does not change and the temperature remains constant at 293 K How much gas in moles has been added if the pressure increases by 0 5 atm 1 atm 1 01 x 105 Nm

Four identical pendulums are made by made by attaching a small ball of mass 100 g on a 20 cm long thread and suspended from the same point Now each ball is given charge Q so that balls move away from each other with each thread making an angle of 45 from the vertical The value of Q is close to 1 41 0 9 10 in SI units A 1 C a 19 Nov 2017 B 1 5 C

Example 5 9 What is the acceleration of the block and trolley system shown in a Fig 5 12 a if the coefficient of kinetic friction between the trolley and the surface is 0 04 What is the tension in the string Take g 10 ms Neglect the mass of the string