Kinetic Theory of Gases Questions and Answers

29 A tank used for filling helium balloons has a volume of 0 300m and contains 2 mol of helium gas at temperature T Considering helium behaves as an ideal gas at T the value of RT 2400J mol where R is universal gas constant The translational kinetic energy of the gas molecules is O A 7200 J O B 2400 J O C 3600 J B 4800 J

A balloon of volume V contains a gas of mass m at a pressure P and temperature 15 C Gas is pumped into the balloon so that its volume is doubled and the pressure is trebled If the temperature increases 6 C in the process find the ratio of the increase in mass to the original mass

Under an adiabatic process the volume of a ideal gas gets doubled Consequently the mea collision time between the gas molecul changes from t to t2 If y for this ga C then a good estimate for 1 5 2 2 is given by

The ratio of specific heat capacity at constant pressure to the specific heat capacity at constant volume is 5 3 for a certain ideal gas 8 m of this gas at an initial pressure of 2 43 105 N m are allowed to expand adiabatically until the volume is 27 m3 At the end of this expansion the pressure of gas is

A vessel of volume V 5 0 litre contains m 1 4 g of nitrogen at a temperature T 1800 K Find the gas pressure taking into account that n 30 of molecules are dissociated into atoms at this temperature A 0 6 atm B 1 2 atm 1 9 atm

N molecules each of mass m of gas A and 2 N molecules each of m ss 2 m of gas B are contained in the same vessel which maintained at a temperature T The mean square of the velocity of molecules of B type is denoted by u and the and the mean square of the X component of the velocity of A type is denoted by w2 u2 is A 2 B 1

5 moles of SO and 5 moles of O react in a closed vessel At equilibrium 60 of the SO is consumed The total number of gaseous moles SO2 O and SO3 in the vessel is a 5 1 b 3 9 c 10 5 d 8 5

ne pv diagram below shows three states 1 2 and 3 of a sample of Helium He gas of mass 2 The atomic mass of helium is 4 0 u The volume of the sample at state 1 V1 is closest to P2 2 0 atm P 657 C 37 C 2 1 Isothermal 3 XZ X

If pressure of a gas contained in a closed vessel is increased by 0 4 when heated by 1 C the initial temperature must be Option 1 Option 2 Option 3 Option 4 250K 250 C 2500K 25 C Assuming ideal gas PV nRT PV nRT O P PARA P Px0 4 V nR T 1 2 PV 1 0 4 on R T 12 0 X T 100 250 k X 0 4 T 1 100 a doubt

A wire of length L and 3 identical cells of negligible internal resistance are connected in series Due to the current the temperature of the wire is raised by AT in a time t A number N of similar cells is now connected in series with a wire of the same material and cross section but of length 2L The temperature of the wire is raised by the same amount AT in the same time t The value of Nis A 4 mCDT H Pxt C 8 B 6 D 9 2001

In two vessels of same volume atomic hydrogen and helium at pressure 1 atm and 2 atm are filled If temperature of both the samples is same then average speed of hydrogen atom UH will be related to helium UHe as A B UH 2 UHe UH UHe

In a cubical vessel are enclosed n molecules of a gas each having a mass m and an average speed u If I is the length of each edge of the cube the pressure exerted by the gas will be A B nmv 7 nm r

If the average mass of a smoke particle in an Indian kitchen is 4 x 10 speed of the smoke particles at 27 C is approximately use k 1 38 x 10 23 J K and 3 1 1 76 1 76 cm sec 1 76 m sec 1 76 km sec None of these 7 kg the rms

The compressibility of a liquid is 4 x 10 8 N m If 2 litre of liquid is subjected to extra pressure of 2 x 106 N m then the decrease in volume of the liquid will be 1 414 cc 421 cc 160 cc

24 Gaseous helium filled in a horizontal fixed cylindrical separated from its surroundings by a piston of finite mass w move without friction Inner surface of the vessel as well as of are coated with a perfectly heat insulating material The pressure is increased rapidly to triple of its initial valu changing the ambient temperature How many times of its in will the volume of helium become when the piston finally sto 3 5 a c 1 3 3 3 5 6 5 7 d 49 3

A cylindrical box is moving with a constant velocity along its axis in a chamber filled with an ideal gas Velocity of the cylinder is so small that it does not produce any turbulence in the gas If absolute temperature of the gas is doubled in what way must speed of the cylinder be changed to keep the drag force unchanged a It must be made 0 354 times of its previous value 2 It must be reduced to half of its previous value c It must be made 0 707 times of its previous value d Drag force does not depend on the temperature of the gas

SolveLancer Test A gas follows the below equation U 3PV U Internal energy P Pressure V Volume How many of the below statement is are correct 1 The gas molecule has more than 1 atom II The gas has 2 atoms in 1 molecule III The gas can have 3 atoms IV For isobaric process Molar specific heat capacity is 4R SolveLancer Test a 1 b 2 c 3

17 Select the incorrect statement about Maxwell s speed distribution 1 The distribution function depends only on the absolute temperature 2 Vrms Vavg Vmp 3 The area under the distribution curve gives total number of molecules of the gas 4 The distribution curve is symmetric about the most probable speed

Consider a closed cylinder whose walls are adiabatic The cylinder lies in a horizontal position and is divided into three parts A A2 and A3 by means of partitions S and S which can move along the length of the cylinder without friction Piston S is adiabatic while S is conducting Initially cach of the parts A A2 and A3 contains one mole of Helium gas at pressure Po temperature To and volume Vo Now heat is slowly supplied to the gas in part A till the temperature in partA3becomes T3 9T0 4 A A S Sz Aa A Volume of leftmost compartment is B Volume of rightmost compartment is 65Vo 27 8V0 27 C Temperature of middle compartment is D Temperature of leftmost compartment is 9To 4 585T 32

When a gas in an open container is heated the mean free path 1 Increases 2 Decreases 3 Remains the same 4 Any of the above depending on the molar mass 171 The translational kinetic energy of oxygen molecules at room temperature is 60 J Their rotational kinetic energy is 1 40 J neet prep Maxwell s speed distribution graph is drawn as shown below The most probable speed of the gas molecules is N 1 4 km s 2 6 8 High Yielding Test Series Part Test 4 v km s Pag Contact Number 9667591930 8527521718

9 004 g The ratio of number of collisions per second at the walls of containers by He and O gas molecule kept at same volume and temperature is assume normal incidence on walls 1 2 1 2 2 1 2 A T 26

1 Figure shows the variation in temperature AT with the amount of heat supplied Q in an isobaric process corresponding to a monoatomic M diatomic D and a polyatomic P gas The initial state of all the gases are the same and the scales for the two axes coincide Ignoring vibrational degrees of freedom the lines a b and c respectively correspond to a P M and D b M D and P c P D and M d D M and P AT b

The temperature of a gas is held constant while its volume is decreased The pressure exerted by the gas on the walls of the container increases because its molecules a strike the walls more frequently b strike the walls with higher velocities c are in contact with the walls for a shorter time d strike the walls with larger force 1996

b 2 567 g per litre c 3 752 g per litre d 4 572 g per litre 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 a T T b c T T 2 d T T PV P V TT PV P V RVT P V T Asteel metre scale is to be ruled so that the millimetre 10

According to kinetic theory of gase molecules of a gas behave like inelastic spheres perfectly elastic rigid spheres perfectly elastic non rigid spheres inclastic non rigid spheres 2014

3 2 2 1 4 1 2 2 2 Nitrogen gas N of mass 28 g is kept in a vessel at pressure of 10 atm and temperature 57 C Due to leakage of N gas its pressure falls to 5 atm and temperature to 27 C The amount of N gas leaked out is 5 1 639 28 3 g 63 2 4 28

4 1 2 2 3 2 2 1 2 Nitrogen gas N of mass 28 g is kept in a vessel at pressure of 10 atm and temperature 57 C Due to leakage of N gas its pressure falls to 5 atm an temperature to 27 C The amount of N gas leake out is 5 1 g 63 3 28 a 2 4 28

4 None of these N molecules of an ideal gas at temperature T and presseure P are contained in a closed box If the molecules in the box gets doubled Keeping total kinetic energy as same then if new pressure is P and temperature is T Then 2 1 P P T T 2 2 2 P P T T 2 2 2 3 P 2 P T T

A given gas is heated from 273 K to 819 K while its volume is tripled If initially the gas pressure is 4 x 105 Pascal the final pressure is A P 4 x 105 Pascal B P 2 x 105 Pascal C P 1 x 105 Pascal D P 0 5 x 105 Pascal E P 0 25 x 105 Pascal

rise For liquid when temperature viscosity of liquid decrease so speed increase in liquid Next for gas when temperature increases it s viscosity increase but unfortunately it s speed increase 8 31 AM V

2 a depth of h 2 cm The pressure required to blow an air bubble out of the lower end of the tube is N m surface tension T 7 10 N m and p 10 kg m The Poisson s ratio of the material of a wire whose volume remains constant under an external normal stress is 3 A uniform metal rope of length Land area of cross section A is suspended from ceiling vertically dis density and Y is Young s modulus of material of the wire respectively Due to its own weight rope sags such the strain energy stored 4 7d g AL is Find value of n nY Water filled into a container with hexagonal cross section of side 3 cmsurface tension of water is 0 02 N m then the surface energy of water will be

For one mole of van der Waal s gas when b 0 and T 300 K the PV vs I V plot is shown below The value of the van der Waal s constant a atm litre mol 2 is Graph not to scale PV tre atm mo 24 6 23 1 21 6 20 1 1 1 0 2 4 5 3 1 5 4 3 0 0 2 0 3 0

Pressure versus temperature graph for a given sample of an ideal gas is as shown Density of gas at A is p then density of gas at B will be PA B 4P Po 14 43 712 20 T 3 To

Calculate the lowest energy of an electron confined in a three dimensional cubical box of each side 1 Find the temperature at which the average energy of the molecules of a perfect gas would be equal to the lowest energy of the electron kB 1 38 x 10 23 J K

d PV 5 16 RT where R is the gas constant 9 A vessel containing 1 mole of O gas molar mass 32 at a temperature T The pressure of the gas is P An identical vessel containing one mole of He gas molar mass 4 at temperature 27 has a pressure of a b P c 2P d 8P 8 20 In a certain region of space there are onli

Questions 1 5 For each question an amount of solute is given and a temperature is stated If all of the solute could be dissolved in 100g of water at the stated temperature would the resulting solution soln be unsaturated saturated or supersaturated 1 60g KCl at 70 C 2 90g KNO3 at 60 C 3 110g NaNO3 at 45 C 4 10g KCIO at 10 C 5 60g NH Cl at 70 C

c Work done on the system is positive d Heat removed from the system is negative thermodynamic process is carried out from an original state D P Nm 200 to an intermediate state 71 A E by the linear process shown in figure The 30 70 Vim total work is done by the gas from D to E to Fis a 100 J b 800 J c 300 d 250 J

A large number of identical elastic balls are moving randomly inside a fixed vertical cylindrical container under a piston that is at a height h 1 0 m above the bottom of the container The container is kept inside a gravity free chamber Root mean square speed of the balls is of the order of 102 m s and mean collision time of the balls is of the order of 10 s The piston is suddenly made to move upwards with a constant velocity u 1 0 m s and stopped at a height 2h above the bottom of the container Find ratio of total internal energy of the balls in the new steady state to that of initial state

Two moles of helium gas is mixed with three moles of hydrogen molecules taken to be rigid What is the molar specific heat of mixture at constant volume Take R 8 3 J moi K a 19 7 J mol K c 17 4 J mol K 2019 Main 12 April I b 15 7 J mol K d 21 6 J mol K

Option C D 1 mol of oxygen 0 at 200 K while the right part contains 1 mol of nitrogen N at 400 K If the stop cork is opened the final temperature upon the mixing of gases will be B A 2R 0 200 K R N 400 K between 295 and 299 K between 301 and 310 K between 199 and 301 K none of these Rate this questio

Reaching a stall angle that causes a reduction in horizontal travel by reducing upward lift pertains to which concept Archimedes principle Bernoulli s principle

Consider a mixture of oxygen and hydrogen at room temperature As compared to hydrogen molecule an oxygen molecule hits the wall With greater average speed With smaller average speed With greater average kinetic energy With smaller average kinetic energy

A quantity of 56g of nitrogen gas is enclosed in a rigid vessel at a temperature 300K The amount of heat in kcal has to be transferred to the gas to increase the root mean square velocity of its molecules 2 0 times is

The mass m 15 g enclosed in a vessel at a temperature T 300 K What amount of heat has to of nitrogen is be transferred to the gas to increase the root mean square velocity of its molecules n 2 0 times

Consider a container of nitrogen gas molecules at 900 K Calculate a the most probable speed b the average speed and c the rms speed for the molecules d State how your results compare with the values displayed in Figure

13 One mole of an ideal monatomic gas is kept in a rigid vessel The vessel is kept inside a steam chamber whose tempreature is 97 C Initially the temperature of the gas is 5 0 C The walls of the vessel have an inner surface of area 800 cm and thickness 10 cm If the temperature of the gas increases to 9 0 C in 5 0 seconds find the thermal conductivity of the material of the walls

4 A balloon is filled at 27 C and 1 atm pressure by 500m He At 3 C and 0 5 atm pressure the volume of He gas contained in balloon will be a 500 b 850 c 900 d 895 volume P If the and tem a P

d 3 4 x 10 J 43 When the container stopped suddenly ordered kineti energy gets converted into disordered kinetic energ which increases the temperature of gas KE per volume is E The pressure exerted by the gas is given ur E 2E 3E E 3 2 2 a 3 b C d

one mole of an ideal monoatomic gas is taken through process AB given by P a BV where a and B are positive constants on P V diagram Which of the following is the correct statement regarding the given process P VA B VB V Temperature is maximum at v Temperature is minimum at v a 3B a 3B At point A rate of increase of temperature of gas with volume is more than at point B Rate of increase of temperature of gas with volume is maximum at v

d 58K ure of n ideal tant pressure d 9 a 4800 K b 3600 K 34 Average velocity of an ideal T a Proportional to b Proportional to T c Proportional to T d Zero 35 The temperatur of c 5000 K d 8000 K molecule is gas 45 A sealed contair expansion cont to 600 K the av a Halved c Doubled 46 If at the same two diatomic of mean kinet