Heat and Gases (Teacher)

8/3/2019 Heat and Gases (Teacher)

1/54

1

Which of the following properties of molecules of an

ideal gas is/are the same on the moon as on the earth, if

the temperature and volume of the gas are unchanged ?

1) The average momentum change when a molecule of

the gas rebounds from a wall of the container.

2) The average kinetic energy of a molecule of the gas.

3) The weight of a molecule of the gas.

A. (1), (2) and (3)B. (1) and (2) only

C. (2) and (3) only

D. (1) only

E. (3) only


2/54

2

The r.m.s. speed of the molecule of a certain gasXis

341 m s-1 at 298 K. Find the molar mass of the gasX.

(Given : Universal gas constantR = 8.31 J mol-1K-1)

A. 5.4 g

B. 21.8 g

C. 33.8 g

D. 42.6 g

E. 63.9 g


3/54

3

The pressure of an ideal gas in a container isP. If the

number of gas molecules is halved, the volume of the

container is doubled and the temperature is kept

constant, the pressure will be

A. P/4

B. P/2C. P

D. 2p

E. 4p


4/54

4

Which of the graphs bestrepresents the distribution

of molecular speeds in a

gas at 500 K if the dottedcurve represents this

distribution for the same

gas at 300 K ?


5/54

5

An ideal gas is contained in acylinder fitted with a light

piston as shown below :

Initially, the piston is held

fixed and the gas is cooled.

Afterwards, the piston is

pushed inwards slowly. Which

of the following graphsrepresents the variation of gas

pressurePwith gas volume V?

(i represents initial state;f

represents final state)


6/54

6

One mole of an ideal gas is contained in a cylinder

fitted with a light, frictionless piston. The gas is heated

under constant pressurePso that its volume increases

from Vto 4Vand the final temperature is T. IfR is the

universal gas constant, the work done by the gas is

4RTE.

3RTD.

RTC3

RTB

43RTA.

.

.


7/54

7

Which of the following is NOT an assumption in deriving thekinetic theory of gases ?

A. The volume of the molecules is negligible compared withthe volume of the gas.

B. Attractive forces between the molecules are negligible.

C. The duration of a collision is negligible compared with the

time between collision.D. Collisions with the walls of the container and with other

molecules cause no change in the average kinetic energy ofmolecules.

E. The molecules suffer negligible change of momentum oncollision with the walls of the container.


8/54

8

An inexpansible vessel contains 1.2 kg of gas at 300 K.

What is the mass of gas expelled from the vessel if it is

heated from 300 K to 400 K under constant pressure ?

A. 0.25 kg

B. 0.3 kgC. 0.6 kg

D. 0.75 kg

E. 0.9 kg


9/54

9

A piston is SLOWLY pushed into a metal cylindercontaining an ideal gas. Which of the followingstatements is INCORRECT ?

A. The mass of the gas remains the same.

B. The pressure of the gas increases.

C. The number of the molecules per unit volumeincreases.

D. The average speed of gas molecules increases.

E. The frequency of collision of the gas moleculeswith the piston increases.


10/54

10

An ideal gas is contained in two metal cylindersA andB connected by a tap, which is initially closed. Thevolume and pressure of the gas in the cylinders are asfollows :

pressure / Pa volume / m 3

A 5 x 105 11 x 10-3

B 2 x 105 4 x 10-3

When the tap connecting the two cylinders is opened,what will be the final pressure in the vessel ? You mayassume that the temperature remains constant.

A. 2.4 x 105

PaB. 3.5 x 105 Pa

C. 4.2 x 105 Pa

D. 5.0 x 105 Pa

E. 6.9 x 105 Pa


11/54

11

For smoke particles undergoing Brownian motion in air,

the motion of the smoke particles is mainly caused by

A. Air convention currents.B. The interaction between oxygen and nitrogen

molecules.

C. Collisions between air molecules.

D. Collisions between smoke particles.

E. Collisions between air molecules and smoke

particles.


12/54

12

1 mole of an ideal mono-atomic gas expands at a

constant pressure of 105 Pa from a volume of 0.02 m3

to a volume of 0.03 m3

. The increase in internalenergy of the gas is

A. 500 J.

B. 667 J.

C. 1000 J.

D. 1500 J.E. 2500 J.


13/54

13

Two vessels of equal volume both

contain an ideal gas and are

connected by a tube of negligible

volume. Initially both vessels are

at temperature To and pressurePo.

One vessel is maintained at To,

while the temperature of the other

is raised to T. The new pressure is

then given by ( )

o

oo

o

o

oo

o

o

o

T

TTPE

TT2TPD

T

PTC

T

TPB

PA.

2.

.

.

.

+

+


14/54

14

Two different gasesA andB are contained in two

identical vessels. If the ratio of their molecular

masses and absolute temperatures are respectively

8 : 1 and 2 : 1, the ratio of their r.m.s. molecular

speeds will be

A. 1 : 4B. 1 : 2

C. 1 : 1

D. 2 : 1

E. 4 : 1


15/54

15

A fixed mass of ideal gas at S.T.P. occupies a volume

of 2 m3. The gas is heated and allowed to expand to a

final volume of 4 m3 with its pressure doubled. The

root mean square speed of the gas molecules is

A. reduced to one quarter to its value.

B. halved.C. unchanged.

D. doubled.

E. increased four times.


16/54

16

Which of the following statements about anexperiment showing the Brownian motion with smoke

particles in air is/are correct ?

1) The motion is caused by collisions between airmolecules and smoke particles.

2) The experiment makes it possible to see the motion

of the air molecules.

3) The motion is irregular because air is a mixture ofgases, and the molecules have different masses.

A. (1), (2) and (3)

B. (1) and (2) only

C. (2) and (3) only

D. (1) only

E. (3) only


17/54

17

An ideal gas is taken through the series of changes shown.Which of the following statements is/are correct ?

1) No net work is done by the gas

is completing one cycle.

2) The work done by the gas

during the changeAB is equal

to that done on the gas duringthe change CD.

3) The gas has the same

temperature atB and C.

A. (1), (2) and (3)B. (1) and (2) only

C. (2) and (3) only

D. (1) only

E. (3) only


18/54

18

An inexpansible vessel contains air at 50C. Whatpercentage of air remains in the vessel if it is heated to

100C under constant pressure ? (You may take theice point to be 273 K)

A. 87 %

B. 85 %

C. 73 %

D. 63 %

E. 50 %


19/54

19

Identical containersA andB contain oxygen (O2) and

hydrogen (H2) respectively. Both gases are at room

temperature and atmospheric pressure. Which of the

following statements is/are true ?

In both containers,

1) the number of gas molecules is the same;2) the r.m.s. speed of gas molecules is the same;

3) the frequency of collision of gas molecules with the

walls of container is the same. A. (1) onlyB. (3) only

C. (1) and (2) only

D. (2) and (3) only

E. (1) , (2) and (3)


20/54

20

Given : Avogadro constant = 6 x 1023 mol-1

Boltzmann constant = 1.38 x 10-23 J K-1

Molar gas constant = 8.31 J mol-1 K-1

If 1 mole of an ideal gas is heated under constant pressure

from 20C to 70C, the total kinetic energy of the gasmolecules is increased by

A. 208 J

B. 415 J

C. 581 J

D. 623 J

E. 831 J


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21

The relative atomic mass of oxygen is 16. what is the

ratio of the average speed of oxygen molecules to that

of hydrogen molecules at room temperature ?

A. 1/16

B. C. 1

D. 4

E. 16


22/54

22

Which of the following statements is/are correct ?

1) The boiling point of pure water increases with

atmospheric pressure.2) The water molecules in 100C steam have a higher

r.m.s. speed than those in pure water boiling at

100C.3) When pure water is boiling, the supplied energybecomes the intermolecular potential energy and

the kinetic energy of the water molecules.A. (1) only

B. (3) only

C. (1) and (2) only

D. (2) and (3) only

E. (1) , (2) and (3)


23/54

23

Two different ideal gases,A andB, are contained intwo identical vessels. If the ratio of their absolutetemperature and the ratio of the root-mean-square

speed of the molecules are respectively 2 : 1 and 3 : 1,the ratio of their molecular mass is

A. 2 : 3B. 2 : 9

C. 1 : 6

D. 9 : 2E. 3 : 2


24/54

24

A fixed mass of an ideal gas undergoes a cycleABCDin which its pressurep and volume Vchange as shownin thep-Vdiagram below. Which of the following

statements is/are correct ?

1) FromA toB, work is done by the gas.

2) FromB to C, heat is extracted from the gas.

3) From CtoD, the internal energy of the gasincreases.

A. (1) only

B. (3) only

C. (1) and (2) only

D. (2) and (3) only

E. (1) , (2) and (3)


25/54

25

When a gas is below its critical temperature, which of

the following is/are correct ?

1) Intermolecular forces are significant.2) The gas can be liquefied by applying pressure

alone.

3) Collisions between molecules are not perfectlyelastic.

A. (1) only

B. (3) onlyC. (1) and (2) only

D. (2) and (3) only

E. (1) , (2) and (3)


26/54

26

The root-mean-square speed of a sample of helium gas

molecules, each of mass m, is c. Which of the following

deductions is correct ?

A. The percentage of molecules travelling at speed c is

greater than at other speeds.

B. Half of the molecules travel at a speed higher than c.C. All molecules travel randomly with speed c.

D. The average speed of the molecules is c.

E. The average kinetic energy of the molecules is mc2.


27/54

27

In which of the following cases will heat always flowaway from a bodyX?

1) Xis changed from its liquid state to a solid at

freezing point.

2) Xis in thermal contact with another system at a

lower temperature.

3) Xis in thermal contact with another system which

has a smaller amount of internal energy.

A. (1) onlyB. (3) only

C. (1) and (2) only

D. (2) and (3) only

E. (1) , (2) and (3)


28/54

28

The internal energy of an ideal gas is always changes

when

1) Its volume increases.2) It undergoes an isothermal change.

3) It is compressed in an insulating container.

A. (1) only

B. (3) only

C. (1) and (2) onlyD. (2) and (3) only

E. (1) , (2) and (3)


29/54

29

Two metallic containersXand Yof volume Vand 4Vrespectively are connected by a narrow tube as shown. Initiallythe tap Sis closed and an ideal gas is contained inXat a

pressure of 400 kPa while containerYis evacuated. The tap Sisthen opened and when equilibrium is finally reached

A. the gas pressure inXis 100 kPa.

B. there are still gas molecules moving through the tap S.

C. the product of pressure and volume of the gas inXis equal

to that in Y.

D. the density of gas molecules inXis greater than that in Y.

E. the gas molecules in Yon average move faster than those in

X.


30/54

30

Which of the following descriptions about ideal gasis/are correct ?

1) An ideal gas obeys Boyles law only under hightemperature and low pressure.

2) The molecules of an ideal gas have no size.

3) The internal energy of an ideal gas consists ofkinetic energy only.

A. (1) only

B. (3) only

C. (1) and (2) only

D. (2) and (3) only

E. (1) , (2) and (3)


31/54

31

A fixed mass of an idealgas undergoes the processABCas shown in thepressure-temperature

diagram. Which of thefollowing deductions fromthe diagram isINCORRECT ?

A. The volume of the gas at Cis greater than that atB.

B. No work is done by thegas when it changes fromA toB.

C. Work is done by the gason the surroundings whenit changes fromB to C.

D. Heat energy is transferredto the gas when it changesfromA toB.

E. Heat energy is extractedfrom the gas when itchanges fromB to C.


32/54

32

A andB are two identical

containers connected by a tap S

initially closed.A contains an

ideal gas at a pressureP1 and a

temperature T1.B contains the

same gas at a pressureP2 and a

temperature T2. The tap Sisthen opened. If the temperature

of the containersA andB

remain constant at T1 and T2

respectively, the final pressureof the gas mixture will be

( )212

2

21

122

21

221

2

.

.

.

.

2

TT

T

P

T

PE

TTTPTPD

TT

TPTPC

PPB

PPA.

1

1

1

1

21

1

+

+

++

+

+

+

+


33/54

33

A vessel of volume 1 x 10-3 m3 contains 0.72 g of an

ideal gas at a pressure of 1 x 105 Pa. The r.m.s.

velocity of the gas molecules is

A. 20 m s-1

B. 110 m s-1

C. 340 m s-1

D. 650 m s-1

E. 3400 m s-1


34/54

34

ContainerXholdsN

molecules of a certain gas

at atmospheric pressure.

Container Y has the same

volume asXand holds 2N

molecules of the same gas.

Both containers are at thesame temperature. The

ratio of the average

number of collisions persecond with the walls inX

to those in Yis

A. 1 :2B. 1 : 2

C. 1 : 1

D. 2 : 1E. 4 : 1


35/54

35

The figure above shows two

curves for a given mass of gasat temperature T1 and T2. If thesymbolsP, Vand Tstand forthe pressure, volume and

absolute temperature of the gas,which of the followingstatements is FALSE ?

A. Temperature T1 is twicetemperature T2.

B. PV/Tis constant for all thepoints on the two curves.

C. When the gas expandsfrom stateB to state Casrepresented by the curveBC, no energy is

transferred from thesurroundings to the gas.

D. No work is done by the gaswhen it changes from state

A to stateB along the lineAB.

E. To take the gas from stateA to state C, work done =100 J.


36/54

36

At 0C temperature and 1.00 x 105N m-2pressure, thedensity of a gas is 0.179 kg m-3. The r.m.s. speed of

the gas molecules at 91C will be

A. 231 m s-1.

B. 470 m s-1.

C. 1290 m s-1.

D. 1490 m s-1.

E. 1730 m s-1.


37/54

37

For an ideal gas expanded isothermally,

A. the work done by the gas is equal to the heatenergy added to it.

B. the work done on the gas is equal to the heat

energy rejected by it.C. the work done on the surroundings is zero.

D. the heat energy transferred to the gas is zero.

E. the internal energy of the gas increases.


38/54

38

An ideal gas undergoes theprocesses marked abc in

the abovep-Vdiagram. If

the total heat energy

supplied to the gas during

the processes is 3100 J, the

change in internal energy

of the gas will be

A. -3900 J.

B. -2700 J.C. 2300 J.

D. 2700 J.

E. 3500 J.


39/54

39

The graph shows thedistribution of molecularspeeds c for a gas at roomtemperature.N(c)represents the number of

molecules

Nin a smallrange of speeds c to c +c so that N = N(c)c. As the temperature is

increased,

A. the peak position will moveto the right and its height

will increase.B. the peak position will move

to the right and its heightwill decrease.

C. the peak position will moveto the left and its heightwill increase.

D. the peak position will moveto the left and its heightwill decrease.

E. the peak position and itsheight will both remainunchanged.


40/54

40

An ideal gas inside a container without thermal

insulation is compressed very slowly to 70 % of its

original volume. While the gas is being compressed,

there is a heat energy transfer of 5000 J. which of the

following statements is/are correct ?

1) Heat energy is transferred out of the system.

2) Work done on the gas during compression is equalto 5000 J.

3) The internal energy increases by 5000 J.

A. (1), (2) and (3)

B. (1) and (2) only

C. (2) and (3) only

D. (1) only

E. (3) only


41/54

41

A fixed mass of an ideal

gas goes through the three

processes fromPto Sindicated in the abovep-T

diagram : (1) :P Q, (2) :

QR, (3) :R S.During which of the above

processes is work done by

the gas on thesurroundings ?

A. (1) only

B. (3) onlyC. (1) and (2) only

D. (1) and (3) only

E. (2) and (3) only


42/54

42

Which of the following statements concerning a realgas is/are correct ?

1) Collisions between molecules and the wall of acontainer are not perfectly elastic.

2) The volume of the molecules cannot be neglected.

3) Intermolecular forces cannot be neglected.

A. (1) only

B. (2) only

C. (3) onlyD. (1) and (2) only

E. (2) and (3) only


43/54

43

The first law of thermodynamic can be expressed asU = Q + W. When as ideal gas is compressed while

keeping its pressure constant, which of the following

holds ?

Q U W

A. positive negative negative

B. positive positive positive

C. zero negative negative

D. negative negative negativeE. negative negative positive


44/54

44

Which of the following is NOT a basic assumption ofthe kinetic theory of an ideal gas ?

A. All molecules are in random motion.

B. All molecules move with the same speed at a

certain temperature.

C. All molecules are point particles that have nophysical size.

D. All collisions are perfectly elastic.

E. All molecules do not exert force on one anotherexcept during collisions.


45/54

45

The graph shows the relation

between the pressurePand the

absolute temperature Tof afixed mass of an ideal gas,

which changes from stateA to

stateB along the pathAB.

Which of the following

statements is/are correct ?

1) The graph shows thatPis

directly proportional to T.

2) The volume Vof the gas

increases.

3) All the points on straight

lineAB satisfy the relationPV/T= constant.

A. (1) onlyB. (3) only

C. (1) and (2) only

D. (2) and (3) only


46/54

46

What is the order of magnitude of the number ofmolecules in 1 cm3 of air in an atmospheric pressure of

105 Pa and at room temperature ?

(Given : Universal gas constant = 8.31 J K-1 mol-1,Avogadro constant = 6.02 x 1023 mol-1)

A. 1025

B. 1019

C. 1016

D. 1013


47/54

47

A fixed mass of an ideal

gas is contained in acylinder with a light piston.

In which of the following

processes will the internal

energy of the gas increase ?

1) The gas is made to expand

under constant pressure.

2) The gas pressure is

increased while keeping

the piston at a fixedposition.

3) The gas is compressed

suddenly as that heat

transfer to or from the gasis negligible.

A. (1) and (2) onlyB. (1) and (3) only

C. (2) and (3) only

D. (1), (2) and (3)


48/54

48

A fixed mass of an ideal gas

undergoes changes from stateXto stateZvia state Yasshown in the plot of pressurepagainst volume Vbelow.

Which graph best shows howthe absolute temperature Tofthe gas varies with its volumeV?


49/54

49

Two vessels contain hydrogen gas and oxygengas respectively. Both gases are assumed to be

ideal and they have the same pressure and

temperature. Which of the following physical

quantities must be the same for the two gases ?

A. The volume of the gasB. The mass per unit volume of the gas

C. The r.m.s. speed of the gas molecules

D. The number of gas molecules per unit volume


50/54

50

A gas in a vessel of fixed volume leaks gradually. Thegas in the vessel changes from stateXto state Yalong

the pathXYshown in the plot of pressure against

absolute temperature. What percentage of the originalmass of gas leaks out from the vessel in this process ?

A. 10 %

B. 20 %C. 25 %

D. 50 %


51/54

51515151

[ 0 6 # 2 2 ] T h e i d e a l g a s e q u a t i o n d e r i v e d f r o m t h e

k i n e t i c t h e o r y c a n b e e x p r e s s e d a s

In this equation, what does the product Nm

r e p r e s e n t ?

A. The total mass of the gas

B. The mass of one mole of the gas

C. The number of molecules in unit volume of the

gas

D. The number of molecules in one mole of the

gas


52/54

52

[07#44] Which of the following thermodynamic

processes on fixed mass of an ideal gas is

IMPOSSIBLE ?

A. It absorbs heat and expands while its internalenergy increases.

B. It absorbs heat and expands while its internal

energy decreases.C. It liberates heat and is compressed while its

internal energy increases.

D. It absorbs heat and is compressed while its

internal energy decreases.


53/54

5353

[08#22] Which of the following assumptionsleads directly to the factor1/3 in deriving the

equationPV=1/3 Nmc2 in kinetic theory of

gases ?A. All gas molecules are in random motion.

B. The gas molecules are negligible in size.

C. All collisions are perfectly elastic.

D. There is no intermolecular force between

molecules except during collision.


54/54

5454

[08#23] A closed vessel contains an ideal gas at

a certain temperature. The gas is heated until its

pressure reaches 1.2 times its initial value.

Calculate the percentage increase in the averagekinetic energy of the gas molecules.

A. 10%

B. 20%

C. 44%

D. It cannot be determined since the number of

moles of gas molecules is not known.

Documents

Heat and Gases (Teacher)