Page 1
JEE Solved Example on Thermodynamics
JEE Mains
Q1: Find the approx. number of molecules contained in a vessel of volume 7 litres at ?? °
?? at
?? . ?? × ????
?? ????????????
(A) ?? . ?? × ????
????
(B) ?? × ????
????
(C) ?? × ????
????
(D) ?? . ?? × ????
????
Ans: (A) ?? = 7 L = 7 × 10
-3
m
3
?? = 273 K
P = 1.3 × 10
5
Pa
? m =
PV
RT
=
1.3 × 10
5
× 7 × 10
-3
8.314 × 273
? 0.4 moles
? No. of molecules = 0.4 × 6.02 × 10
23
= 2.4 × 10
23
molecules
Q2: An ideal gas mixture filled inside a balloon expands according to the relation ????
?? /?? =
constant. The temperature inside the balloon is
(A) Increasing
(B) Decreasing
(C) Constant
(D) Can't be said
Ans: (A) PV
2/3
= const.
?
nRT
V
V
2/3
= const.
? TV
-1/3
= const.
? T = conts. × V
1/3
? On increasing volume, temperature increase
Q3: A rigid tank contains ???? ???? of nitrogen at ?? ?????? . Sufficient quality of oxygen is supplied to
increase the pressure to ?? ?????? , while the temperature remains constant. Amount of oxygen
supplied to the tank is:
(A) ?? ????
(B) ???? ????
(C) ???? ????
(D) ???? ????
Ans: (C) T = constant, V = constant,
Page 2
JEE Solved Example on Thermodynamics
JEE Mains
Q1: Find the approx. number of molecules contained in a vessel of volume 7 litres at ?? °
?? at
?? . ?? × ????
?? ????????????
(A) ?? . ?? × ????
????
(B) ?? × ????
????
(C) ?? × ????
????
(D) ?? . ?? × ????
????
Ans: (A) ?? = 7 L = 7 × 10
-3
m
3
?? = 273 K
P = 1.3 × 10
5
Pa
? m =
PV
RT
=
1.3 × 10
5
× 7 × 10
-3
8.314 × 273
? 0.4 moles
? No. of molecules = 0.4 × 6.02 × 10
23
= 2.4 × 10
23
molecules
Q2: An ideal gas mixture filled inside a balloon expands according to the relation ????
?? /?? =
constant. The temperature inside the balloon is
(A) Increasing
(B) Decreasing
(C) Constant
(D) Can't be said
Ans: (A) PV
2/3
= const.
?
nRT
V
V
2/3
= const.
? TV
-1/3
= const.
? T = conts. × V
1/3
? On increasing volume, temperature increase
Q3: A rigid tank contains ???? ???? of nitrogen at ?? ?????? . Sufficient quality of oxygen is supplied to
increase the pressure to ?? ?????? , while the temperature remains constant. Amount of oxygen
supplied to the tank is:
(A) ?? ????
(B) ???? ????
(C) ???? ????
(D) ???? ????
Ans: (C) T = constant, V = constant,
?? ?? =
35
28
= 1.25 Kmoles
?
?? ?? =
????
?? = const.
?
?? ?? ?? ?? =
?? ?? ?? ?? ? ?? ?? =
?? ?? ?? ?? × ?? ?? =
9
6
×
35
28
˜ 1.875 kmoles
? Moles of O
2
supplied
= 1.875 - 1.25 = 0.625kmoles
? Amount of oxygen = 20 kg
Q4: At temperature ???? , the pressure of ?? . ?? ?? argon in bulb is ?? . The bulb is put in a bath having
temperature higher by ???? ?? than the first one. ?? . ?? ?? of argon gas had to be removed to
maintained original pressure. The temperature ?? is equal to
(A) ?????? ??
(B) ?????? ??
(C) ?????? ??
(D) ???? ??
Ans: (B) ???? =
4
?? ????
???? =
( 4 - 0.8)
?? ?? ( ?? + 50) =
3.2?? ?? ( ?? + 50)
By (i) and (ii) we get,
4
?? ???? =
3.2?? ?? ( ?? + 50) ? 4?? = 3.2?? + 3.2 × 50
? ?? = 200 ??
Q5: When 2 gms of a gas are introduced into an evacuated flask kept at ????
°
?? the pressure is found
to be one atmosphere. If ???????? of another gas added to the same flask the pressure becomes 1.5
atmosphere. The ratio of the molecular weights of these gases will be
(A) ?? : ??
(B) 3:1
(C) ?? : ??
(D) ?? : ??
Ans: (A) For P = 1 atm , m
1
= 2gms , T = 298 K
? 1 × ?? =
2?? ?? 1
× 298
For ?? = 1.5 atm, ?? 1
= 2gm , ?? 2
= 3gm , ?? = 298 K.
Page 3
JEE Solved Example on Thermodynamics
JEE Mains
Q1: Find the approx. number of molecules contained in a vessel of volume 7 litres at ?? °
?? at
?? . ?? × ????
?? ????????????
(A) ?? . ?? × ????
????
(B) ?? × ????
????
(C) ?? × ????
????
(D) ?? . ?? × ????
????
Ans: (A) ?? = 7 L = 7 × 10
-3
m
3
?? = 273 K
P = 1.3 × 10
5
Pa
? m =
PV
RT
=
1.3 × 10
5
× 7 × 10
-3
8.314 × 273
? 0.4 moles
? No. of molecules = 0.4 × 6.02 × 10
23
= 2.4 × 10
23
molecules
Q2: An ideal gas mixture filled inside a balloon expands according to the relation ????
?? /?? =
constant. The temperature inside the balloon is
(A) Increasing
(B) Decreasing
(C) Constant
(D) Can't be said
Ans: (A) PV
2/3
= const.
?
nRT
V
V
2/3
= const.
? TV
-1/3
= const.
? T = conts. × V
1/3
? On increasing volume, temperature increase
Q3: A rigid tank contains ???? ???? of nitrogen at ?? ?????? . Sufficient quality of oxygen is supplied to
increase the pressure to ?? ?????? , while the temperature remains constant. Amount of oxygen
supplied to the tank is:
(A) ?? ????
(B) ???? ????
(C) ???? ????
(D) ???? ????
Ans: (C) T = constant, V = constant,
?? ?? =
35
28
= 1.25 Kmoles
?
?? ?? =
????
?? = const.
?
?? ?? ?? ?? =
?? ?? ?? ?? ? ?? ?? =
?? ?? ?? ?? × ?? ?? =
9
6
×
35
28
˜ 1.875 kmoles
? Moles of O
2
supplied
= 1.875 - 1.25 = 0.625kmoles
? Amount of oxygen = 20 kg
Q4: At temperature ???? , the pressure of ?? . ?? ?? argon in bulb is ?? . The bulb is put in a bath having
temperature higher by ???? ?? than the first one. ?? . ?? ?? of argon gas had to be removed to
maintained original pressure. The temperature ?? is equal to
(A) ?????? ??
(B) ?????? ??
(C) ?????? ??
(D) ???? ??
Ans: (B) ???? =
4
?? ????
???? =
( 4 - 0.8)
?? ?? ( ?? + 50) =
3.2?? ?? ( ?? + 50)
By (i) and (ii) we get,
4
?? ???? =
3.2?? ?? ( ?? + 50) ? 4?? = 3.2?? + 3.2 × 50
? ?? = 200 ??
Q5: When 2 gms of a gas are introduced into an evacuated flask kept at ????
°
?? the pressure is found
to be one atmosphere. If ???????? of another gas added to the same flask the pressure becomes 1.5
atmosphere. The ratio of the molecular weights of these gases will be
(A) ?? : ??
(B) 3:1
(C) ?? : ??
(D) ?? : ??
Ans: (A) For P = 1 atm , m
1
= 2gms , T = 298 K
? 1 × ?? =
2?? ?? 1
× 298
For ?? = 1.5 atm, ?? 1
= 2gm , ?? 2
= 3gm , ?? = 298 K.
? 1.5 × ?? = [
2
?? 1
+
3
?? 2
] ?? × 298
Using (ii)/(i) we get,
1.5 =
[
2
?? 1
+
2
?? 2
]
2
?? 1
? 3 = [2 +
3?? 1
?? 2
] ?
?? 1
?? 2
=
1
3
Q6: During an experiment, an ideal gas obeys an addition equation of state ?? ?? ?? = constant. The
initial temperature and pressure of gas are ?? and ?? respectively. When it expands to volume ?? ?? ,
then its temperature will be?
(A) T
(B) v ?? ??
(C) ?? ??
(D) ?? v ?? ??
Ans: (B) ?? =
?????? ?? ? (
?????? ?? )
2
?? = constant ?
?? 2
?? = constant
? ?? ?? = (
?? ?? ?? ?? )
1
2
× ?? ?? = v 2??
Q7: A barometer tube, containing mercury, is lowered in a vessel containing mercury until only
???? ???? of the tube is above the level of mercury in the vessel. If the atmospheric pressure is ???? ????
of mercury, what is the pressure at the top of the tube?
(A) ???? . ????????
(B) ???? . ????????
(C) ?? . ??????????
(D) ?? . ??????????
Ans: (A) ?? at top of tube
+ ?? due to 50 cm of Hg
= ?? atmospheric
? ?? at top of tube
= ( 75 - 50) cm of Hg
= 25 cm of Hg
= 25 ×
10
5
75
Pa = 33.3kPa
Page 4
JEE Solved Example on Thermodynamics
JEE Mains
Q1: Find the approx. number of molecules contained in a vessel of volume 7 litres at ?? °
?? at
?? . ?? × ????
?? ????????????
(A) ?? . ?? × ????
????
(B) ?? × ????
????
(C) ?? × ????
????
(D) ?? . ?? × ????
????
Ans: (A) ?? = 7 L = 7 × 10
-3
m
3
?? = 273 K
P = 1.3 × 10
5
Pa
? m =
PV
RT
=
1.3 × 10
5
× 7 × 10
-3
8.314 × 273
? 0.4 moles
? No. of molecules = 0.4 × 6.02 × 10
23
= 2.4 × 10
23
molecules
Q2: An ideal gas mixture filled inside a balloon expands according to the relation ????
?? /?? =
constant. The temperature inside the balloon is
(A) Increasing
(B) Decreasing
(C) Constant
(D) Can't be said
Ans: (A) PV
2/3
= const.
?
nRT
V
V
2/3
= const.
? TV
-1/3
= const.
? T = conts. × V
1/3
? On increasing volume, temperature increase
Q3: A rigid tank contains ???? ???? of nitrogen at ?? ?????? . Sufficient quality of oxygen is supplied to
increase the pressure to ?? ?????? , while the temperature remains constant. Amount of oxygen
supplied to the tank is:
(A) ?? ????
(B) ???? ????
(C) ???? ????
(D) ???? ????
Ans: (C) T = constant, V = constant,
?? ?? =
35
28
= 1.25 Kmoles
?
?? ?? =
????
?? = const.
?
?? ?? ?? ?? =
?? ?? ?? ?? ? ?? ?? =
?? ?? ?? ?? × ?? ?? =
9
6
×
35
28
˜ 1.875 kmoles
? Moles of O
2
supplied
= 1.875 - 1.25 = 0.625kmoles
? Amount of oxygen = 20 kg
Q4: At temperature ???? , the pressure of ?? . ?? ?? argon in bulb is ?? . The bulb is put in a bath having
temperature higher by ???? ?? than the first one. ?? . ?? ?? of argon gas had to be removed to
maintained original pressure. The temperature ?? is equal to
(A) ?????? ??
(B) ?????? ??
(C) ?????? ??
(D) ???? ??
Ans: (B) ???? =
4
?? ????
???? =
( 4 - 0.8)
?? ?? ( ?? + 50) =
3.2?? ?? ( ?? + 50)
By (i) and (ii) we get,
4
?? ???? =
3.2?? ?? ( ?? + 50) ? 4?? = 3.2?? + 3.2 × 50
? ?? = 200 ??
Q5: When 2 gms of a gas are introduced into an evacuated flask kept at ????
°
?? the pressure is found
to be one atmosphere. If ???????? of another gas added to the same flask the pressure becomes 1.5
atmosphere. The ratio of the molecular weights of these gases will be
(A) ?? : ??
(B) 3:1
(C) ?? : ??
(D) ?? : ??
Ans: (A) For P = 1 atm , m
1
= 2gms , T = 298 K
? 1 × ?? =
2?? ?? 1
× 298
For ?? = 1.5 atm, ?? 1
= 2gm , ?? 2
= 3gm , ?? = 298 K.
? 1.5 × ?? = [
2
?? 1
+
3
?? 2
] ?? × 298
Using (ii)/(i) we get,
1.5 =
[
2
?? 1
+
2
?? 2
]
2
?? 1
? 3 = [2 +
3?? 1
?? 2
] ?
?? 1
?? 2
=
1
3
Q6: During an experiment, an ideal gas obeys an addition equation of state ?? ?? ?? = constant. The
initial temperature and pressure of gas are ?? and ?? respectively. When it expands to volume ?? ?? ,
then its temperature will be?
(A) T
(B) v ?? ??
(C) ?? ??
(D) ?? v ?? ??
Ans: (B) ?? =
?????? ?? ? (
?????? ?? )
2
?? = constant ?
?? 2
?? = constant
? ?? ?? = (
?? ?? ?? ?? )
1
2
× ?? ?? = v 2??
Q7: A barometer tube, containing mercury, is lowered in a vessel containing mercury until only
???? ???? of the tube is above the level of mercury in the vessel. If the atmospheric pressure is ???? ????
of mercury, what is the pressure at the top of the tube?
(A) ???? . ????????
(B) ???? . ????????
(C) ?? . ??????????
(D) ?? . ??????????
Ans: (A) ?? at top of tube
+ ?? due to 50 cm of Hg
= ?? atmospheric
? ?? at top of tube
= ( 75 - 50) cm of Hg
= 25 cm of Hg
= 25 ×
10
5
75
Pa = 33.3kPa
Q. 8 A vessel contains 1 mole of ?? ?? gas (molar mass 32) at a temperature ?? . The pressure of the
gas is ?? . An identical vessel containing one mole of He gas (molar mass 4) at a temperature ?? ?? has
a pressure of
(A) ?? /??
(B) ??
(C) ?? ??
(D) ????
Ans: (C)
Q9: The ratio of average translational kinetic energy to rotational kinetic energy of a diatomic
molecule temperature ?? is
(A) 3
(B) ?? /??
(C) ?? /??
(D) ?? /??
Ans: (D) For diatomic molecule
Translational degree of freedoms = 3
Rotational degree of freedoms = 2
Ratio =
3????
2????
=
3
2
Page 5
JEE Solved Example on Thermodynamics
JEE Mains
Q1: Find the approx. number of molecules contained in a vessel of volume 7 litres at ?? °
?? at
?? . ?? × ????
?? ????????????
(A) ?? . ?? × ????
????
(B) ?? × ????
????
(C) ?? × ????
????
(D) ?? . ?? × ????
????
Ans: (A) ?? = 7 L = 7 × 10
-3
m
3
?? = 273 K
P = 1.3 × 10
5
Pa
? m =
PV
RT
=
1.3 × 10
5
× 7 × 10
-3
8.314 × 273
? 0.4 moles
? No. of molecules = 0.4 × 6.02 × 10
23
= 2.4 × 10
23
molecules
Q2: An ideal gas mixture filled inside a balloon expands according to the relation ????
?? /?? =
constant. The temperature inside the balloon is
(A) Increasing
(B) Decreasing
(C) Constant
(D) Can't be said
Ans: (A) PV
2/3
= const.
?
nRT
V
V
2/3
= const.
? TV
-1/3
= const.
? T = conts. × V
1/3
? On increasing volume, temperature increase
Q3: A rigid tank contains ???? ???? of nitrogen at ?? ?????? . Sufficient quality of oxygen is supplied to
increase the pressure to ?? ?????? , while the temperature remains constant. Amount of oxygen
supplied to the tank is:
(A) ?? ????
(B) ???? ????
(C) ???? ????
(D) ???? ????
Ans: (C) T = constant, V = constant,
?? ?? =
35
28
= 1.25 Kmoles
?
?? ?? =
????
?? = const.
?
?? ?? ?? ?? =
?? ?? ?? ?? ? ?? ?? =
?? ?? ?? ?? × ?? ?? =
9
6
×
35
28
˜ 1.875 kmoles
? Moles of O
2
supplied
= 1.875 - 1.25 = 0.625kmoles
? Amount of oxygen = 20 kg
Q4: At temperature ???? , the pressure of ?? . ?? ?? argon in bulb is ?? . The bulb is put in a bath having
temperature higher by ???? ?? than the first one. ?? . ?? ?? of argon gas had to be removed to
maintained original pressure. The temperature ?? is equal to
(A) ?????? ??
(B) ?????? ??
(C) ?????? ??
(D) ???? ??
Ans: (B) ???? =
4
?? ????
???? =
( 4 - 0.8)
?? ?? ( ?? + 50) =
3.2?? ?? ( ?? + 50)
By (i) and (ii) we get,
4
?? ???? =
3.2?? ?? ( ?? + 50) ? 4?? = 3.2?? + 3.2 × 50
? ?? = 200 ??
Q5: When 2 gms of a gas are introduced into an evacuated flask kept at ????
°
?? the pressure is found
to be one atmosphere. If ???????? of another gas added to the same flask the pressure becomes 1.5
atmosphere. The ratio of the molecular weights of these gases will be
(A) ?? : ??
(B) 3:1
(C) ?? : ??
(D) ?? : ??
Ans: (A) For P = 1 atm , m
1
= 2gms , T = 298 K
? 1 × ?? =
2?? ?? 1
× 298
For ?? = 1.5 atm, ?? 1
= 2gm , ?? 2
= 3gm , ?? = 298 K.
? 1.5 × ?? = [
2
?? 1
+
3
?? 2
] ?? × 298
Using (ii)/(i) we get,
1.5 =
[
2
?? 1
+
2
?? 2
]
2
?? 1
? 3 = [2 +
3?? 1
?? 2
] ?
?? 1
?? 2
=
1
3
Q6: During an experiment, an ideal gas obeys an addition equation of state ?? ?? ?? = constant. The
initial temperature and pressure of gas are ?? and ?? respectively. When it expands to volume ?? ?? ,
then its temperature will be?
(A) T
(B) v ?? ??
(C) ?? ??
(D) ?? v ?? ??
Ans: (B) ?? =
?????? ?? ? (
?????? ?? )
2
?? = constant ?
?? 2
?? = constant
? ?? ?? = (
?? ?? ?? ?? )
1
2
× ?? ?? = v 2??
Q7: A barometer tube, containing mercury, is lowered in a vessel containing mercury until only
???? ???? of the tube is above the level of mercury in the vessel. If the atmospheric pressure is ???? ????
of mercury, what is the pressure at the top of the tube?
(A) ???? . ????????
(B) ???? . ????????
(C) ?? . ??????????
(D) ?? . ??????????
Ans: (A) ?? at top of tube
+ ?? due to 50 cm of Hg
= ?? atmospheric
? ?? at top of tube
= ( 75 - 50) cm of Hg
= 25 cm of Hg
= 25 ×
10
5
75
Pa = 33.3kPa
Q. 8 A vessel contains 1 mole of ?? ?? gas (molar mass 32) at a temperature ?? . The pressure of the
gas is ?? . An identical vessel containing one mole of He gas (molar mass 4) at a temperature ?? ?? has
a pressure of
(A) ?? /??
(B) ??
(C) ?? ??
(D) ????
Ans: (C)
Q9: The ratio of average translational kinetic energy to rotational kinetic energy of a diatomic
molecule temperature ?? is
(A) 3
(B) ?? /??
(C) ?? /??
(D) ?? /??
Ans: (D) For diatomic molecule
Translational degree of freedoms = 3
Rotational degree of freedoms = 2
Ratio =
3????
2????
=
3
2
Q10 : One mole of an ideal gas at STP is heated in an insulated closed container until the average
speed of its molecules is doubled. Its pressure would therefore increase by factor.
(A) 1.5
(B) v ??
(C) 2
(D) 4
Ans: (D) We know
?? rms
= 1.085v
avg
? v
3?? ?? = 1.085v
avg
; ?? is density
In this case ?? is constant
? ?? ? ( ?? avg
)
2
?
?? ?? ?? ?? = [
( ?? avg
)
?? ( ?? avg
)
?? ]
2
= 4
Q11: One mole of an ideal gas is contained within a cylinder by a frictionless piston and is initially
at temperature ?? . The pressure of the gas is kept constant while it is heated and its volume
doubles. If ?? is molar gas constant, the work done by the gas in increasing its volume is?
(A) ???? ???? ??
(B) ?? /?? RT
(C) RT
(D) ?? /?? RT
Ans: (C) Frictionless piston means, no generation of heat due to the motion of piston.
n = 1
T
i
= T
P = const.
?? i
= V ?? f
= 2 V
Initially: - ???? = ????
Work done = P?V = P( 2 V - V) = PV = RT
Q12: A polyatomic gas with six degrees of freedom does ???? ?? work when it is expanded at
constant pressure. The heat given to the gas is?
(A) ?????? ??
(B) ?????? ??
(C) ?????? ??
(D) ?????? ??
Ans: (A) ?? = 6
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