Physics 73 1st Probset 2nd Sem 13-14

8/13/2019 Physics 73 1st Probset 2nd Sem 13-14

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PHYSICS 73

1stLong Probset

2nd semesterAY 2013 - 2014

University of te Pi!i""ines

Co!!ege of S#ien#e


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I$S%&UC%I'$S( Choose the bestanswer and shade the corresponding circle in

your answer sheet. To change your answer, cross-out and sign your originalanswer and then shade your new answer.

US)*UL C'$S%A$%S(

ideal gas constant: R= 8.314 J/ol! = "."8#"$ %at/ol!

&olt'ann constant: k= 1.3811"-#3J/olecule!

(te)an-&olt'ann constant: = *.$+1"-8/#!4

1 atosphere = 1."11"*ascal

1""" liter = 1 3

ogadro0s nuer: 2= $."## 1"#3 olecules/ol

I$*'&+A%I'$ A,'U% A%)&(

noral )ree'ing point = #+3.1* ! = ".""oCnoral oiling point = 3+3.1* ! = 1"".""oC

triple-point teperature = #+3.1$ ! = "."1

o

Cspeci)ic heat li5uid water6 = 4.171"3J/g!

speci)ic heat ice6 = #.1"1"3 J/g!

latent heat o) )usion = 3.341"* J/g

latent heat o) apori'ation = #.#*$1"$ J/g

Hour 2

1. The pressure of a gas at the triple point of water isP. The gas is warmed at

constant volume until the pressure is 3P. What is the final Celsiustemperature as compared to the temperature of the triple point of water in

Celsius?

A. greater by a factor of more than

!. greater by a factor of C. greater by a factor between 1 and

". lesser by a factor of 1#

$. the same

2. A temperature change of 1% C& was observed' what is the corresponding

temperature change in the (ahrenheit scale?A. )% (&

!. 2* (&

C. 1% (&

". )% (&

$. % (&

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Hour

. A %mby %msolid s,uare ob-ect has a hole in the middle of radius 2m. f

the ob-ect is cooled with a small finite temperature change' what will happen

to the radius of the circular hole?A. decreases

!. increases

C. remains the same

". answer depends on the coefficient of linear e/pansion of the material

$. answer depends on the magnitude of the temperature change

*. A 10 cylindrical flas is filled to the brim with glycerin at 3&C. When thetemperature of the system is raised to )3&C' 14 m of glycerin spills out of the

flas.5iven that the coefficient of volume e/pansion of glycerin is *4 / 13 0%

601' determine the coefficient of linear e/pansion of the flas.

A. 7.* / 130*601

!. .2 / 130*601

C. 1.% / 130%601

". 3.8 / 130%601

$. 3.% / 130%601

Hour *

%. 233 g of steam and 233 g of li,uid water' both of which have a temperature

of 133.3&C' are cooled to a temperature of 3.3&C. Which among the two

substances will release more heat?A. i,uid Water

!. 9teamC. :either will release any heat

". !oth will release an e,ual amount of heat

$. There is insufficient data to answer this ,uestion.

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7. 1% g of ice at 3 &C is mi/ed with 23 g of steam at 133 &C in a thermallyisolated vessel and allowed to reach thermal e,uilibrium. What is the final

temperature of the resulting mi/ture?

A. 2%8 &C

!. 02) &C

C. 2% &C

". 3 &C$. 133 &C

). A 3.31 g iron nail is driven into a board by a 2.33 g hammer that

increases its temperature. The speed of the hammer as it hits the nail is %.33

m#s. f %3; of the inetic energy delivered by the hammer is transformed into

heat that flows into the nail and does not flow out' what is the temperature

increase of the nail after it is struc once? c ron< *)3 = # g 6A. 13.7* C&!. %.2 C&

C. 2.77 C&

". 3.% C&

$. 3.33 C&

Hour %

8. Which of the following statements about heat transfer is T>$?

. Conduction re,uires the motion of atoms from one region to another

. Convection re,uires a fluid to transfer heat. >adiation does not re,uire a medium to transfer heat

A. only

!. only

C. only". and

$. ' and

4. Three different metal rods 1' 2 and conduct the same amount of heat per

unit time if their ends are sub-ected to the same temperature gradient. Arrange

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the thermal conductivities of the metals in "$C>$A9:5 order if theirphysical dimensions are@

etal rod 1@ cross0sectional area S' lengthL

etal rod 2@ cross0sectional area 3.%S' length 2L

etal rod @ cross0sectional area S' length 2L

A. 1' 2'

!. 2' ' 1C. 2' 1'

". 1' ' 2

$. ' 2' 1

13. A tungsten sphere with radius 2 cm is suspended in a large evacuated

room with walls at 33 6. f you want to maintain the temperature of the

sphere at 2333 6' 182 W of power input is needed. What is the emissivity oftungsten?

A. 1.3

!. 3.8

C. 3.)

". 3.*$. 3.3

Hour 7

11. 9ome n moles of ideal gas at pressureP' was heated isobarically so that its

temperature rose from T1 to T2. What is the final volume occupied by the gas?A. nRT2

2# BPT1

!. nRT2 #P

C. nRT12# BPT2

". nRT2 #P$. Cannot be determined

12. Two identical cylinders are filled with different ideal gases having the

same pressure and temperature. Which of the following statements is T>$

regarding the setups?

A. The total mass of gas is the same in both cylinders.

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!. The total number of gas molecules is the same in both cylinders.C. !oth gases have the same density.

". All of the above

$. :one of the above

1. A cylinder contains 3.133 mol of an ideal monoatomic gas. nitially the

gas is at a pressure of 1.33 / 13%Da and occupies a volume of 2.%3 / 130m.f the gas is allowed to e/pand at constant pressure to twice the initial volume'

find the final temperature.A. 732 6

!. 31 6

C. 1%3 6

". 1812 6

$. 72 6

Hour )

1*. A rigid vessel contains some amount of ideal gas. The density and

pressure of the gas was determined to beandP' respectively. What is the

vrmsof the molecules of the gas?

A. BP#B31/2

!. B2RP#1/2

C. BRk#P1/2

". B3P#1/2

$. B3k#P1/2

1%. The molar mass of carbon mono/ide CE is 28.3 g#mol. f the temperature

is 33 6' what is the fraction of CE molecules with speeds between 13 m#sand )2% m#s?

v#vrms fraction v#vrms fraction

3.23 3.311 1.23 3.))1

3.*3 3.3)) 1.*3 3.882

3.73 3.218 1.73 3.4*)

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3.83 3.*11 1.83 3.4)4

1.33 3.738 2.33 3.44

A. 3.77*

!. 3.882C. 3.218

". 3.44

$. 3.333

17. 9uppose a container filled with Helium gas is maintained at a temperature

of *33 6. What is the average translation inetic energy of a Helium atom

according to the inetic molecular theory?

A. 8.24 / 13021=!. 2.)7 / 13021=

C. %.%2 / 13021=

". 1.8 / 13023=

$. 1.4 / 13023=

Hour 8

1). 9ome nmoles of hydrogen gas' a diatomic gas' is ept in a closed cubic

vessel of constant volume V. The initial temperature was measured to be T. f

some ,uantity of heat Qis absorbed by the gas' what is the final temperature

of the gas?

A. T + 2Q / (5nR)!. T + 2Q / (3nR)C. T - 2Q / (5nR)

". T - 2Q / (3nR)

$. T

18. Derfectly rigid containers each hold nmoles of ideal gas' one being

hydrogen BH2 and other being neon B:e. f it taes 133 = of heat to increase

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the temperature of the hydrogen by 2.%3 C&' by how many degrees will thesame amount of heat raise the temperature of the neon? Assume that the heat

capacities of H2and :e follow the e,uipartition theorem.

A. *.1) C&

!. 1.%3 C&

C. 1.43 C&

". 8.31 C&$. *.81 C&

14. 9uppose it was determined that the gas molecules of a sample has the

following degrees of freedom@ three translational' two vibrational and three

rotational. According to the e,uipartition theorem' what is the sampleFs heat

capacity?

A. *>!. 8>C. )#2 >

". >

$. %#2 >

Hour 4

23. Consider some n moles of ideal gas at some initial temperature and

pressure' T andP1' respectively. f the gas was compressed isothermally to a

higher pressureP2' how much wor was done by the gas?

A. GnRT lnBP2#P1!. 2nRT lnBP2#P1

C. nRT lnBP2#P1

". G2nRT lnBP2#P1

$. 3

21. Three moles of an ideal monoatomic gas e/pands at a constant pressure of2.%3 atm the volume of the gas changes from .23 / 1302mto *.%3 / 1302m.

Calculate the amount of wor the gas does in e/panding.

A. .28 =

!. 0.28 =

C. 3.32% =

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". 1.1 =$. 14.** =

22. 9uppose an ideal gas' initially at pressurePand volume V' can e/pand to a

final volume 2Vvia any thermodynamic process. Which thermodynamic

process will yield the highest amount of wor done by the gas?

A. isobaric!. isothermal

C. isochoric

". adiabatic

$. free e/pansion

2. Ene mole of an ideal gas is initially at 1.2 / 13%Da and 3.3 m. The gas is

then heated at constant pressure resulting to an 83 C& increase in temperature.What is the wor done by the system?A. 77% =

!. 077% =

C. %71 =

". 1.2 =

$. 1%% =

Hour 13

2*. 9ome nmoles of ideal gas at a temperature T and occupying a volume V1'

underwent a cyclic process. (irstly' it underwent an isothermal e/pansion sothat its new volume is V2. :e/t' it was compressed bac to the original state

such that this process traces out a straight line in thepV diagram. How much

heat flowed into the system during this cycle?

A. nRT lnBV1# V2 I nRTBV12I V22 # BV2V1!. nRT lnBV2# V1 0 nRTBV1

20 V22 # B*V2V1

C. nRT lnBV2# V1 0 nRTBV1G V2". nRT lnBV1# V2 I nRTBV1 I V2

$.nRT lnBV2# V1 I nRTBV120 V2

2 # B2V2V1

2%. An ideal gas e/pands while the pressure is ept constant. What is the

direction of the heat flow?

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A. into the gas!. out of the gas

C. no heat involved

". cannot be determined

$. constant temperature

Hour 11

27. 9ome amount of ideal gas with ratio of heat capacities ,is at pressure and

temperature'P1and T1' respectively. f it was compressed adiabatically to a

final temperature T2'whatis the final pressure of the gas?

A.P1 BT2# T11 / (1 - )

!. BP1 T2# T11 -

C.P1 BT2# T1 / (1 - )

".P1 BT2# T11 / ( - 1)

$.P1 BT2# T1 / ( - 1)

2). An ideal monoatomic gas is initially at a pressure of 1.33 / 13%Da' volume

of 2.%3/130 m and temperature of 31 6. f the gas is allowed to e/pand

adiabatically to twice the initial volume' calculate the change in internal

energy per mole.A. 014% =#mol

!. 2214 =#mol

C. 02%)* =#mol

". 184 =#mol

$. 1%1% =#mol

Hour 12

28. 9uppose an e/perimental engine has an efficiency of 3.2%. f the engine

burns erosene Bheat of combustion < *.723 / 13)=#g at a rate of %33 mg percycle' how much wor does it deliver per cycle?

A. %.8 / 13 =

!. %.8 / 137=

C. 1.2 / 13)

=

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". 2. / 13* =$. 1.) / 13* =

24. An engine operating using the Etto cycle has an efficiency of 3.%.

Assume that its woring substance is purely a diatomic gas. What is the

compression ratio of this engine?

A. 2.4!. 1.*

C. 1.4

". 1.7

$. %.3

Hour 1

3. A window air0conditioner unit absorbs 4.83 / 13*= of heat per minute

from the room being cooled and in the same time period deposits 1.** / 13%=

of heat into the outside air. What is the coefficient of performance?

A. 2.1

!. 1.*)C. 3.78

". 3.*)

$. .1

1. "uring one summer season' your friend suggested that to cool down your

room' you eep all doors and windows closed while setting your refrigerator

to the lowest temperature and eep its door open. Why is your friendFs idea

not plausible?A. The temperature difference between your room and refrigerator is very

large.

!. The refrigerator taes heat from the room but throws it right bac to the

room.

C. arge power input is needed to cool your room.

". The temperature difference between your room and refrigerator is small.$. The refrigerator cannot wor if its door is ept open.

Hour 1*

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2. Two adiabatic curves intersect once on a DJ diagram. A cycle could be

completed by creating a thermodynamic path between the two adiabatic

curves. Which of the following added thermodynamic paths would follow the

second law of thermodynamics?

A. isobaric

!. isochoricC. isothermal

". none of the above

$. all of the above

. Which of the following statements is (A9$?

A. The second law of thermodynamics states that it is impossible to achieveabsolute Kero with a finite number of steps.

!. The 6elvin0Dlanc statement and the Clausius statements are e,uivalent.

C. The coefficient of performance of a refrigerator can be less than 1.

". The spontaneous transfer of heat from a cold reservoir to a hot reservoir is

impossible.$. The efficiency of any engine is always positive.

Hour 1%

*. A copper pot at room temperature is filled with room0temperature water.

magine a process whereby the water spontaneously freeKes and the potbecomes hot. This process violates?

A. The first law of thermodynamics only.

!. The second law of thermodynamics only.

C. The first and second laws of thermodynamics.". The conservation of energy.

$. The second law of thermodynamics and the conservation of energy.

%. A Carnot heat engine has a thermal efficiency of 3.733' and thetemperature of its hot reservoir is 833 6. f 333 = of heat is re-ected to the

cold reservoir in one cycle' what is the amount of heat input from the hot

reservoir during one cycle?

A. )%33 =

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!. %333 =C. 23 =

". 1233 =

$. 1833 =

7. What is the ma/imum possible efficiency of heat engine operating

between TC < 2%&C and TH < 443&C?A. )7;

!. %;C. 4);

". 2*;

$. %7;

). Which of the following are parts of a Carnot cycle for a Carnotrefrigerator BTHL TC?

. sothermal e/pansion at TH. Adiabatic e/pansion to TC. sothermal compression at THJ. Adiabatic compression to TC

A. and only

!. and J only

C. and only". and J only

$. :one of the above

Hour 17

8. Three moles of an ideal gas undergo a reversible isothermal compression

at 23.3 &C. "uring this compression' 18%3 = of wor is done on the gas. Whatis the change of entropy of the gas?

A. 07.1 =#6

!. 0).78 =#6

C. 42.%3 =#6". 3.1% =#6

$. 8.87 =#6

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4. A container' filled with 3.2%3 g of water at 8%.3 &C' is inside a room at23 &C. The water eventually cools to the room temperature. The cooling

process is essentially isothermal for the air in the room. Calculate the total

entropy change of the waterIair

A. 22 =#6

!. 0**2 =#6

C. 14* =#6". 1888 =#6

$. 0*414 =#6

*3. 9uppose you want to observe the resulting change in entropy of a liter of

water as it undergoes an increase in temperature. Arrange the change in

entropy of the water as its temperature

. goes from 23 &C to *3 &C. goes from 2% &C to %3 &C. goes from 3 &C to %3 &C

A. L L

!. L L

C. L <

". L L

$. < L

Hour 1)

*1. A configuration of molecules underwent a change in entropy!S. Whatis the ratio between the final and initial number of microstates?

A.!S#k

!. "-!S#

C. lnB!S#k)". k lnB!S)

$. "!S#

*2. Two moles of an ideal gas occupy a volume V. The gas e/pandsisothermally and reversibly to a volume V. What is the change in entropy of

the system?

A. 018.2) =#6

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!. 04.1 =#6C. 4.1 =#6

". 11.% =#6

$.18.2) =#6END OF EXAM

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Physics 73 1st Probset 2nd Sem 13-14