Thermodynamics Notes and MCQs

Notes 29 Pages

Joint Entrance Examination (Main)

Physics

Contributed by

Yash Kuruvilla

259
SUMMARY

Thermal equilibrium, teroth law of thermodynamics, Concept of temperature.

Heat, work and internal energy. First law of thermodynamics.

Second law of thermodynamics, reversible and irrevessible processes.
Isothermal and adiabatic process.

Carnot engine and its efficency Refrigerators.

0 0 0 0
C 0 F 32 C F
100 180 100 180
   
  

w P V 
(Isothesmal process)

RT

n
1
2
v
v
(Isothesmal process)
PV = Const (Isothesmal process)
P v

=

Const (adiabasic process)
P
1-
T

= Const
TV
-1
= Constant
r =
cv
cp
Monoatomic gases
v p
3 5
C = R, = C = R,
2 2


= 1.67
Diatomic gases
v p
5 7
γ
C = R, C = R, = 1.4
2 2
Polgatomic gases
v p
7R 9R
C = , C = ,
2 2

= 1.4
1 1 2 2
1
W = (P V P V )
γ
1


(adiabafic Process)
1 2
R (T T )
=
γ
1
m 


Q u W    
(First law of thermodynamics)
Q U Cv t   
(V = Const)
Q Cp t  
( P = Const)
u 0 
(isothesmal process cyelic process)
Page 1
260

Coefricent of Performance of refrigesatos
1
Q
W
n 
1 2
1
Q Q
Q



1 2
1
T T
T



Coefcient of performance of refrigetors.
2
Q
w
 
2
1 2
Q
Q Q


2
1 2
T
T T



I deal gas
Cp Cv R 
1. A difference of temperature of 25
0
C is equivalent to a difference of
(A) 72
0
F (B) 45
0
F (C) 32
0
F (D) 25
0
F
2. What is the value of absolute temperature on the Celsius Scale ?
(A) -273.15
0
C (B) 100
0
C (C) -32
0
C (D) 0
0
C
3. The temperature of a substance increases by 27
0
C What is the value of this increase of Kelvin
scale?
(A) 300K (B) 2-46K (C) 7 K (D) 27 K
4. At Which temperature the density of water is maximum?
(A) 4
0
F (B) 42
0
F (C) 32
0
F (D) 39.2
0
F
5. The graph AB Shown in figure is a plot of a temperature of a body in degree Fahrenhit than slope
of line AB is
(A)
9
5
(B)
5
9
(C)
9
1
(D)
9
3
Page 2
261
6. The temperature on celsius scale is 25
0
C What is the corresponding temperature on the Fahrenheit
Scale?
(A) 40
0
F (B) 45
0
F (C) 50
0
F (D) 77
0
F
7. The temperature of a body on Kelvin Scale is found to be x.K.when it is measured by Fahrenhit
thesmometes. it is found to be x
0
F, then the value of x is .
(A) 313 (B) 301.24 (C) 574-25 (D) 40
8. A Centigrade and a Fahrenhit thesmometes are dipped in boiling wates-The wates temperature is
lowered until the Farenhit thesmometes registered 140
0
what is the fall in thrmometers
(A) 80
0
(B) 60
0
(C) 40
0
(D) 30
0
9. A uniform metal rod is used as a bas pendulum. If the room temperature rises by 10
0
C

and the
efficient of line as expansion of the metal of the rod is,
6 1
C
2 10 0
 

what will have percentage increase
in the period of the pendulum ?
(A) -2

10
-3
(B) 1

10
-3
(C) -1

10
-3
(D) 2

10
-3
10. A gas expands from 1 litre to 3 litre at atmospheric pressure. The work done by the gas is about
(A) 200 J (B) 2 J (C) 300 J (D) 2

10
5
J
11. Each molecule of a gas has f degrees of freedom. The radio
P
V
C
γ
=
C
for the gas is
(A)
1
2
f

(B)
1
1
f

(C)
2
1
f

(D)
 
1
1
3
f 

12. Is the cyclic Process Shown on the V

P diagram, the magnitude of the work done is

(A)
2
12
2
PP








(B)
2
12
2
VV








(C)
 
2 2 1 1
P V PV


(D)
  
1212
VVPP
4


13. If the ratio of specific heat of a gas at Consgant pressure to that at constant volume is , the Change
in internal energy of the mass of gas, when the volume changes from V to 2V at Constant Pressure
p, is
(A)
γ
1
PV

(B)
γ
1
R

(C) PV (D)
γ
PV
γ
1
Page 3
262
14. The change in internal energy, when a gas is cooled from 927
0
C

³ to 27
0
C
(A) 200% (B) 100% (C) 300% (D) 400%
15. For hydrogen gas Cp - Cv = a and for oxygen gas Cp - Cv = b, The relation between a and b is
given by
(A) a = 4b (B) a = b (C) a = 16b (D) a = 8b
16. In a thermodynamic process, pressure of a fixed mass of a gas is changed in such a manner that the
gas release 20J of heat and 8J of work has done on the gas- If the inifial internal energy of the gas
was 30j, then the final internal energy will be
(A) 58 J (B) 2 J (C) 42 J (D) 18 J
17. If for a gas
cv
cp
= 1.67, this gas is made up to molecules which are
(A) diatomic (B) Polytomic
(C) monoatomic (D) mixnese of diatomic and polytomic molecules
18. An ideal monoatomic gas is taken around the cycle ABCDA as Shown in the
P V
diagram. The
work done during the cycle is given by
(A) PV (B)
2
1
PV (C) 2 PV (D) 4 PV
19. A given mass of a gas expands from state A to B by three different paths 1, 2 and 3 as shown in the
figure. If W
1
,W
2
and W
3
respectively be the work done by the gas along the three paths, then
(A) W
1
>W
2
>W
3
(B) W
1
<W
2
<W
3
(C) W
1
=W
2
=W
3
(D) W
1
<W
2
, W
1
<W
3
20. One mole of a monoatomic gas
5
γ
3
 

 
 
is mixed with one mole of A diatomic gas
7
γ
5
 

 
 
what
will be value of  for mixture ?
(A) 1-454 (B) 1-4 (C) 1-54 (D) 1-5
21. If du represents the increase in internal energy of a thesmodynamic system and dw the work done
by the system, which of the following statement is true ?
(A) du = dw in isothermal process (C) du = - dw in an aidabadic process
(B) du = dw in aidabadic process (D) da = - dw in an isothermal process
Page 4
263
22. One mole of a monoatomic ideal gas is mixed with one mole of a diatomic ideal gas The molas
specific heat of the micture at constant volume is ..........
(A) 4 R (B) 3 R (C) R (D) 2R
23. One mole of a monoatomic gas is heate at a constant pressure of 1 atmosphere from 0k to 100 k.
If the gas constant R = 8.32 J/mol k the change in internal energy of the gas is approximate ?
(A) 23 J (B) 1.25

10
3
J (C) 8.67

10
3
J (D) 46 J
24. A gas mixture consists of 2 mde of oxygen and 4 mole of argon at tempressure T.Neglecting all
vibrational modes, the total internal energy of the system is
(A) 11 RT (B) 9 RT (C) 15 RT (D) 4 RT
25. A monoatomic ideal gas, initially at temperature T
1
is enclosed in a cylindes fitted with a frictionless
piston. The gas is allowed to expand adiabatically to a temperature T
2
by releasing the piston suddenly
If L
1
and L
2
the lengths of the gas colum be fore and afters expansion respectively, then then
2
1
T
T
is
given by
(A)
2
3
1
2
L
L
 
 
 
(B)
2
3
2
1
L
L
 
 
 
(C)
1
2
L
L
(D)
2
1
L
L
26. Starting with the same intial Conditions, an ideal gas expands from Volume V
1
to V
2
in three different
ways. The Work done by the gas is W
1
if the process is purely isothermal, W
2
if purely isobasic and
W
3
if purely adiabatic Then
(A) W
2
>W
1
>W
3
(B) W
2
>W
3
>W
1
(C) W
1
>W
2
>W
3
(D)W
1
>W
3
>W
2
27. In a given process on an ideal gas dw = 0 and dQ < 0. Then for the gas
(A) the volume will increase (B) the pressure will semain constant
(C) the temperature will decrease (D) the temperature will increase
28. Wafer of volume 2 filter in a containes is heated with a coil of 1kw at 27
0
C. The lid of the containes
is open and energy dissipates at the late of
J
160
S
. In how much time tempreture will rise from
27
0
C to 77
0
C.

Specific heat of wafers is

4.2
Kg
KJ
(A) 7 min (B) 6 min 2s (C) 14 min (D) 8 min 20 S
Page 5
264
29. 70 calorie of heat are required to raise the temperature of 2 mole of an ideal gas at constant pressure
from 30
0
C to 35
0
C
The amount of heat required to raise the temperature of the same gas through the same range at
constant volume is .................. calorie.
(A) 50 (B) 30 (C) 70 (D) 90
30. When an ideal diatomic gas is heated at constant pressure, the Section of the heat energy supplied
which increases the infernal energy of the gas is..
(A)
7
3
(B)
5
3
(C)
5
2
(D)
7
5
31. Two cylinders A and B fitted with piston contain equal amounts of an ideal diatomic gas at 300 k.
The piston of A is free to move, While that of B is held fixed. The same amount of heat is given to the
gas in each cylindes. If the rise in temperature of the gas in A is 30K, then the rise in temperature of
the gas in B is.
(A) 30 K (B) 42 K (C) 18 K (D) 50 K
32. An insulated containes containing monoatomic gas of molas mass Mo is moving with a velocity, V.If
the container is suddenly stopped, find the change in temperature.
(A)
2
Mov
5R
(B)
2
Mov
4R
(C)
2
Mov
3R
(D)
2
Mov
2R
33. A Small spherical body of radius r is falling under gravity in a viscous medium. Due to friction the
medium gets heated. How does the late of heating depend on radius of body when it attains terminal
velocity!
(A) r
2
(B) r
3
(C) r
4
(D) r
5
34. The first law of thermodynamics is concerned with the conservation of
(A) momentum (B) energy (C) mass (D) temperature
35. If heat given to a system is 6 k cal and work done is 6kj. The change in internal energy is .......... KJ.
(A) 12.4 (B) 25 (C) 19.1 (D) 0
36. The internal energy change in a system that has absorbed 2 Kcal of heat and done 500J of work is
(A) 7900 J (B) 4400 J (C) 6400 J (D ) 8900 J
37. Which of the following is not a thermodynamical function.
(A) Enthalpy (B) Work done
(C) Gibb's energy (D) Internal energy
38. Which of the following is not a thermodynamic co-ordinate.
(A) R (B) P (C) T (D) V
39. The work of 62-25 KJ is performed in order to compress one kilo mole of gas adiabatically and in
this process the temperature of the gas increases by 5
0
C The gas is _______ R = 8-3
J
molk
(A) triatomic (C) monoatomic
(B) diatomic (D) a mixture of monoatomic and diatomic
Page 6
265
40. Cp and Cv denote the specific heat of oxygen per unit mass at constant Pressure and volume
respectively, then
(A) cp - cv =
16
R
(B) Cp - Cv = R
(C) Cp - Cv = 32 R (D) Cp - Cv =
32
R
41. When a System is taken from State i to State f along the path iaf, it is found that Q = 70 cal and w
= 30 cal, along the path ibf. Q=52cal. W atoug the path ibf is
(A) 6 cal (B) 12 cal (C) 24 cal (D) 8 cal
42. One kg of adiatomic gas is at a pressure of

5
2
N
5 10
m

The density of the gas is
3
5kg
m
what is the
energy of the gas due to its thermal motion ?
(A) 2.5

10
5
J (B) 3.5

10
5
J (C) 4.5

10
5
J (D) 1.5

10
5
J
43. 200g of water is heated from 25
0
C
0
45
0
C Ignoring the slight expansion of the water the change in its
internal energy is (Specific heat of wafer
C9
cal
1
0
)
(A) 33.4 KJ (B) 11.33 KJ (C) 5.57 KJ (D) 16.7 KJ
44. During an adiabatic process, the pressure of a gas ifound to be propostional to the fifth power of its
absolute temperature. The radio
cv
cp
for the gas is
(A)
5
4
(B)
4
3
(C)
4
5
(D) 4
45. One mole of oxygen is heated at constant pressure stasting at 0
0
C. How much heat energy in cal
must be added to the gas to double its volume ? Take R = 2
cal
molk
(A) 1938 (B) 1920 (C) 1911 (D) 1957
46.

moles of a gas filled in a containes at temperature T is in equilibrium inidially - If the gas is
compressed slowly and is thesmally to half its initial volume the work done by the atmosphere on the
piston is
(A)
µRT
-
2
(B)
2
RT
(C) RT ln (2 -
2
1
) (D) –RTln
2
Page 7
266
47. Heat capacity of a body depends on the .......... as well as on ..........
(A) material of the body, its mass (C) mass of the body, itd temperature
(B) material of the body, its temperature (D) Volume of the body, its mass
48. In thesmodynamics, the work done by the system is considered ......... and the work done on the
system is Considered ...........
(A) Positive, zero (B) nagative, Positive
(C) zero, negative (D) Positive, negative
49. A thesmodynamic system goes from States
(i) P,V to 2P, V (ii) P,V to P, 2V. Then what is work done in the two Cases.
(A) Zero, PV (B) Zero, Zero (C) PV, Zero (D) PV,PV
50. For free expansion of the gas which of the following is true ?
(A) Q = 0, W > 0 and

Eint = -W (B) W = 0, Q >0 and

Eint = Q
(C) W > 0, Q < 0 and

Eint = 0 (D) Q = W = 0 and

Eint = 0
51. For an adiabatic process involving an ideal gas
(A) P

– 1
= T

– 1
= constant (B) P
1 –


= T


= constant
(C) PT

– 1
= constant (D) P

– 1
T

= constant
52. Figure shows four P

V diagrams. which of these curves represent.
isothermal and adiabatic processes ?
(A) A and C (B) A and B (C) C and D (D) B and D
53. An ideal gas is taken through cyclic process as shown in the figure. The net work done by the gas is
(A) PV (B) 2 PV (C) 3 PV (D) zero
54.

moles of gas expands from volume VV
1
to V
2
at constant temperature T. The work done by the gas
is
(A) RT








1
2
V
V
(B) RT ln








1
2
V
V
n
(C) RT








1
V
V
1
2
(D) RT ln








1
V
V
n
1
2
Page 8
267
55. A Cyclic Process ABCD is Shown in the P

V diagam. which of the following curves represent
the same Process ?
(A) (B) (C) (D)
56. A Cyclic process is Shown in the P

T diagram.
Which of the curve show the same process on a V

T diagram ?
(A) (B)
(C) (D)
57. One mole of an ideal gas
p
v
C
γ
C

at absolute temperature T
1
is adiabatically compressed from an
initial pressure P
1
to a final pressure P
2
The resulting temperature T
2
of the gas is given by.
(A)
γ
γ 1
2
2 1
1
p
T = T
p

 
 
 
(B)
γ
1
γ
2
2 1
1
p
T = T
p

 
 
 
(C)
γ
2
2 1
1
p
T = T
p
 
 
 
(D)
γ
1
2
2 1
1
p
T = T
p

 
 
 
Page 9
268
58. An ideal gas is taken through the cycle A

B

C

A as shown in the figure. If the net heat
supplied to the gas in the cycle is 5J, the work done by the gas in the process C

A is
(A) - 5 J (B) -10 J (C) -15 J (D) - 20 J
59. In anisothermal reversible expansion, if the volume of 96J of oxygen at 27
0
C is increased from 70
liter to 140 liter, then the work done by the gas will be
(A) 300 R log
e
(2)
(B) 81 R log
e
(2)
(C)
2
10
200 R og
(D) 100 R log
10
(2)
60. For an iso thermal expansion of a Perfect gas, the value of
P
P

is equal to
(A)
1
2
ΔV
- γ
V
(B)
ΔV
γ
V

(C)
2
ΔV
γ
-
V
(D)
ΔV
γ
V

61. For an aidabatic expansion of a perfect gas, the value of
P
P
is equal to
(A)
Δr
- γ
v
(B)
v
v

(C)
2
Δv
-γ
v
(D)
Δv
γ
-
v
62. If r denotes the ratio of adiabatic of two specific heats of a gas. Then what is the ratio of slope of an
adiabatic and isothermal
P V
curves at their point of intersection ?
(A)
1
γ
(B) -1 (C)  (D)  + 1
63. Work done permol in an isothermal ? change is
(A)
2
1
log
v
RT e
v
(B)
1
2
v
v
10logRT
(C)
2
1
v
v
10logRT
(D)
2
1
v
v
elogRT
64. The isothermal Bulk modulus of an ideal gas at pressure P is
(A)
vP (B) P (C)
2
p
(D)
p
v
65. The isothermal bulk modulus of a perfect gas at a normal Pressure is
(A) 1.013

10
6
2
m
N
(B)
2
11
m
N
10013.1


(C)
2
5
m
N
10013.1 
(D)
2
11
m
N
10013.1 
Page 10

Thermodynamics Notes and MCQs

Thermodynamics Notes and MCQs

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