Physics 2C Summer Session II
Quiz #3
Multiple Choice. Choose the answer that best completes the
statement or answers the question.
1. A monatomic ideal gas goes through the Carnot cycle shown in the
…gure. The pressure and volume at point A are PA = 1400kP a and VA = 10L
respectively. The volumes at C and D are VC = 24L and VD = 15L:
Carnot Cycle
The volume at point B is
A) 12L B) 14L C) 15L D) 16L E) 18:3L
In a Carnot cycle the volume ratios VB =VA and VC =VD are equal. Hence
VB = VA (VC =VD ) = 10 (24=15) = 16L ! D
2. The pressure at point C is
A) 445kP a B) 875kP a C) 712kP a D) 496kP a E) 794kP a
For an adiabatic expansion from point B the pressure at C is given by
PC = PB (VB =VC ) ;
where PB = PA VA =VB . Hence
PC = 1400
10
5=3
(16=24)
= 445:2kP a ! A
16
3. The shaded area enclosed inside the cycle is
1
A) 6580J B) 1558J C) 4482J D) 5022J E) 11600J
The shaded area is the work done during one cycle. This is given by
W
W
W
= PA VA ln (VB =VA ) PC VC ln (VC =VD )
= (PA VA PC VC ) ln (1:6) = (1400 10
= 1558J ! B
445:2
24) ln (1:6)
4. If the temperature of the hot isothermal process AB is Th = 440 C,
what is the temperature, Tc , of the cool isothermal process CD?
A) 224 C B) 302 C C) 236 C D) 336 C E) 271 C
There are numerous ways to obtain this temperature. A relatively simple
procedure is
Tc
Th
Tc
Qc
Wc
445:2 24 ln 1:6
= :7632
=
=
Qh
Wh
1400 10 ln 1:6
= :7632 (440 + 273) = 544K = 271 C ! E
=
:
5. If this Carnot cycle is run in reverse as a refrigerator its coe¢ cient
of performance, COP; is
A) 2:46 B) 2:88 C) 3:22 D) 4:67 E) 5:45
The coe¢ cient of performance for a refrigerator is de…ned as COP = Qc =W =
Qc = (Qh Qc ) : For this refrigerator the COP is
COP
=
COP
=
Qc
Qh
Tc
=
=
PC V C
PA VA PC VC
Qc
Th Tc
445:2 24
= 3:22 ! C
1400 10 445:2 24
6. Venus has an atmosphere that is essentially all carbon dioxide (CO2 ;
amu = 44) with a pressure at the surface of P = 9:3 106 P a. The mean
temperature at the surface is T = 460 C. What is the speed of sound in this
atmosphere if the speci…c heat at constant volume for CO2 is Cv = 4R?
A) 330m=s B) 416m=s C) 440m=s D) 480m=s E) 518m=s
For an ideal gas
P
= kT =m = RT =mmol :
The speci…c heat ratio is
=
Cp
Cv + R
=
= 1:25:
Cv
Cv
2
Hence the speed of sound on Venus is
p
p
p
vs =
P= =
RT =mmol = 1:25
8:314
(460 + 273) =:044 = 416m=s ! B
7. A horizontal string of mass 750g and length 2:5m is tied to a wall
on one end and with a pulley supports a weight W at the opposite end. If the
mathematical form of a wave traveling on this string is
y = 4 sin 2 (x=24:5
40t) ;
where x is measured in cm and t in seconds, what is the value W of the weight?
A) 29N B) 2:94N C) :80N D) 80N E) 44N
The velocity of the wave on the string is v = 24:5 40 = 980:0cm=s = 9:8m=s
The mass/length of the string is = :75=2:5 = :3kg=m: Since v 2 = F= we …nd
2
F = W = (9:8) :3 = 28:8N: ! A
8. The string described in problem 7 now supports a weight of 30N:
Standing waves on this string all have nodes at both ends. The frequency of the
third harmonic standing wave is
A) 2Hz B) 3Hz C) 4Hz D) 6Hz E) 12Hz
The wavelengths of a standing wave are given by n = 2L=n: The frequencies
associated with these standing waves are given by p
fn = v= n : Since the velocity
of a wave on this string supporting 30N is v = 30=:3 = 10m=s: Hence the
frequency of the third harmonic is
f3 = 10=
3
=3
10
= 6Hz: ! D
5
9. The change in entropy when 3kg of water at T = 80 C is mixed with
1kg of water at T = 20 C is
A) 36J=K B) 2325J=K C) 143J=K D) 416J=K
The …nal equilibrium temperature is found from
3cwat (80
T ) = cwat (T
E) 53J=K
20) ! T = 65 C:
The change in entropy is found from
Z 65+273
Z 65+273
dT
dT
s = 3cwat
+ cwat
80+273 T
20+273 T
65 + 273
65 + 273
s = cwat 3 ln
+ ln
= :0126cwat
80 + 273
20 + 273
s = :0126 4184 = 52:7J=K ! E
3
10. At a distance of 3m from a sound source the intensity level is 78dB.
What is the intensity level (in dB) at a distance of 12m?
A) 66dB B) 72dB C) 60dB D) 46dB
The intensity level falls o¤ as 1=r2 ; hence
E) 50dB
2
I12
1= (12)
= :0625
=
I3
1=32
The change in dB is
= 10 log :0625 =
Hence the dB level is 78dB
12:04dB
12dB = 66dB: ! A
Some useful constants
2
3
Boltzmann’s constant k = 1:38 10 23 J=K
4Universal gas constant
R = 8:314J=Kmol 5
Speci…c heat of water cwat = 4184J=kg K
Some useful equations
PV
= N kT = nRT;
U =Q
W; W =
P dV; 2L = (n + 1=2) n
Z
dQ
!t) ; 2L = n n ; s =
T
Cp
; Q = mc T; y = A sin (kx
Cv
p
3
= const; hKEi = kT; vs =
P= ; ! = vk;
2
=
PV
Z
4
= 10 log I=I0