DC Pandey Solutions (JEE Advance): Thermometry, Thermal Expansion | DC Pandey Solutions for JEE Physics PDF Download

 Page 1


For JEE Advanced 
Objective Questions 
  Single Correct Option 
Q 1.  The average velocity of molecules of a gas of molecular weight M at temperature T is 
 (a) 
3RT
M
   (b) 
8RT
M ?
   (c) 
2RT
M
   (d) zero 
Q 2.  Four particles have velocities 1,0,2 and 3 m/s. The root mean square velocity of the particles 
(definition wise) is 
  (a) 3.5 m/s   (b) 3.5 m / s   (c) 1.5m/s   (d) 
14
m / s
3
 
Q 3.  A steel rod of length 1 m is heated from 25° to 75°C keeping its length constant. The longitudinal 
strain developed in the rod is (Given coefficient of linear expansion of steel = 12 × 10
-6
/°C) 
  (a) 6 × 10
-4
   (b) -6 × 10
-5
   (c) -6 × 10
-4
   (d) zero 
Q 4.  In a process the pressure of a gas remains constant. If the temperature is doubled, then the change 
in the volume will be  
  (a) 100%   (b) 200%   (c) 50%   (d) 25% 
Q 5.  The average kinetic energy of the molecules of an ideal gas at 10°C has the value E. The 
temperature at which the kinetic energy of the same gas becomes 2E is 
  (a) 5°C   (b) 10°C  (c) 40°C   (d) None of these 
Q 6.  A polyatomic gas with n degrees of freedom has a mean energy per molecule given by 
 (a) 
n
RT
2
   (b) 
1
RT
2
   (c) 
n
kT
2
   (d) 
1
kT
2
 
Q 7.  The temperature of an ideal gas is increased from 27°C to 927°C. The rms speed of its molecules 
becomes 
  (a) twice   (b) half   (c) four times   (d) one-fourth 
Q 8.  In case of hydrogen and oxygen at NTP, which of the following is the same for both?  
  (a) Average linear momentum per molecule (b) Average KE per molecule 
  (c) KE per unit volume    (d) KE per unit mass 
Q 9.  Two thermally insulated vessels 1 and 2 are filled with air at temperatures (T1, T2 ), volumes (V1, 
V2) and pressures (P1, P2) respectively. If the valve joining the two vessels is opened, the 
temperature inside the vessel at equilibrium will be (P = common pressure) 
  (a) T1 + T2   (b) (T1 +T2)/2  (c) 
1 2 1 2
1 1 2 2 2 1
T T P(V V )
P V T P V T
?
?
  (d) 
1 2 1 1 2 2
1 1 2 2 2 1
T T (P V P V )
P VT P V T
?
?
 
Q 10.  Two marks on a glass rod 10 cm apart are found to increase their distance by 0.08 mm when the 
rod is heated from 0°C to 100°C. A flask made of the same glass as that of rod measures a volume 
of 100 cc at 0°C. The volume it measures at 100°C in cc is 
  (a) 100.24   (b) 100.12  (c) 100.36   (d) 100.48 
Page 2


For JEE Advanced 
Objective Questions 
  Single Correct Option 
Q 1.  The average velocity of molecules of a gas of molecular weight M at temperature T is 
 (a) 
3RT
M
   (b) 
8RT
M ?
   (c) 
2RT
M
   (d) zero 
Q 2.  Four particles have velocities 1,0,2 and 3 m/s. The root mean square velocity of the particles 
(definition wise) is 
  (a) 3.5 m/s   (b) 3.5 m / s   (c) 1.5m/s   (d) 
14
m / s
3
 
Q 3.  A steel rod of length 1 m is heated from 25° to 75°C keeping its length constant. The longitudinal 
strain developed in the rod is (Given coefficient of linear expansion of steel = 12 × 10
-6
/°C) 
  (a) 6 × 10
-4
   (b) -6 × 10
-5
   (c) -6 × 10
-4
   (d) zero 
Q 4.  In a process the pressure of a gas remains constant. If the temperature is doubled, then the change 
in the volume will be  
  (a) 100%   (b) 200%   (c) 50%   (d) 25% 
Q 5.  The average kinetic energy of the molecules of an ideal gas at 10°C has the value E. The 
temperature at which the kinetic energy of the same gas becomes 2E is 
  (a) 5°C   (b) 10°C  (c) 40°C   (d) None of these 
Q 6.  A polyatomic gas with n degrees of freedom has a mean energy per molecule given by 
 (a) 
n
RT
2
   (b) 
1
RT
2
   (c) 
n
kT
2
   (d) 
1
kT
2
 
Q 7.  The temperature of an ideal gas is increased from 27°C to 927°C. The rms speed of its molecules 
becomes 
  (a) twice   (b) half   (c) four times   (d) one-fourth 
Q 8.  In case of hydrogen and oxygen at NTP, which of the following is the same for both?  
  (a) Average linear momentum per molecule (b) Average KE per molecule 
  (c) KE per unit volume    (d) KE per unit mass 
Q 9.  Two thermally insulated vessels 1 and 2 are filled with air at temperatures (T1, T2 ), volumes (V1, 
V2) and pressures (P1, P2) respectively. If the valve joining the two vessels is opened, the 
temperature inside the vessel at equilibrium will be (P = common pressure) 
  (a) T1 + T2   (b) (T1 +T2)/2  (c) 
1 2 1 2
1 1 2 2 2 1
T T P(V V )
P V T P V T
?
?
  (d) 
1 2 1 1 2 2
1 1 2 2 2 1
T T (P V P V )
P VT P V T
?
?
 
Q 10.  Two marks on a glass rod 10 cm apart are found to increase their distance by 0.08 mm when the 
rod is heated from 0°C to 100°C. A flask made of the same glass as that of rod measures a volume 
of 100 cc at 0°C. The volume it measures at 100°C in cc is 
  (a) 100.24   (b) 100.12  (c) 100.36   (d) 100.48 
Q 11.  The given curve represents the variation of temperature as a function of volume for one mole of an 
ideal gas. Which of the following curves best represents the variation of pressure as a function of 
volume? 
 
  (a)   (b)   (c)   (d) 
Q 12.  A gas is found to obey the law P V = constant. The initial temperature and volume are T0 and V0. 
If the gas
 
expands to a volume 3 V0, then the final temperature becomes 
 (a) 
0
3T   (b) 
0
2T   (c) 
0
T
3
   (d) 
0
T
2
 
Q 13.  Air fills a room in winter at 7°C and in summer at 37°C. If the pressure is the same in winter and 
summer, the ratio of the weight of the air filled in winter and that in summer is 
  (a) 2.2    (b) 1.75   (c) 1.1    (d) 3.3 
Q 14.  Three closed vessels A, B and C are at the same temperature T and contain gases which obey 
Maxwell distribution law of velocities. Vessels contains O2, B only N2 and C mixture of equal 
quantities of O2 and N2. If the average speed of the O2 molecules in vessel A is v 1 that of N2 
molecules in vessel B is v2, then the average speed of the O2 molecules in vessel C is 
  (a) 
12
(v v )
2
?
   (b) v1    (c) 
12
vv   (d) None of these 
Q 15.  In a very good vacuum system in the laboratory, the vacuum attained was 10
-13
 atm. If the 
temperature of the system was 300 K, the number of molecules present in a volume of 1 cm is 
  (a) 2.4 × 10
6  
(b) 24   (c) 2.4 × 10
9
   (d) zero 
Q 16.  If nitrogen gas molecule goes straight up with its rms speed at 0°C from the surface of the earth 
and there are no collisions with other molecules, then it will rise to an approximate height of 
  (a) 8 km   (b) 12 km   (c) 12 m   (d) 8 m 
Q 17.  The coefficient of linear expansion of steel and brass are 11 × 10
-6
/°C and 19 × 10
-6
/°C 
respectively. If their difference in lengths at all temperatures has to kept constant at 30 cm, their 
lengths at 0°C should be  
  (a) 71.25 cm and 41.25 cm    (b) 82 cm and 52 cm 
  (c) 92 cm and 62 cm     (d) 62.25 cm and 32.25 cm 
Q 18.  The given P-U graph shows the variation of internal energy of an ideal gas with increase in 
pressure. Which of the following pressure-volume graph is equivalent to this graph? 
Page 3


For JEE Advanced 
Objective Questions 
  Single Correct Option 
Q 1.  The average velocity of molecules of a gas of molecular weight M at temperature T is 
 (a) 
3RT
M
   (b) 
8RT
M ?
   (c) 
2RT
M
   (d) zero 
Q 2.  Four particles have velocities 1,0,2 and 3 m/s. The root mean square velocity of the particles 
(definition wise) is 
  (a) 3.5 m/s   (b) 3.5 m / s   (c) 1.5m/s   (d) 
14
m / s
3
 
Q 3.  A steel rod of length 1 m is heated from 25° to 75°C keeping its length constant. The longitudinal 
strain developed in the rod is (Given coefficient of linear expansion of steel = 12 × 10
-6
/°C) 
  (a) 6 × 10
-4
   (b) -6 × 10
-5
   (c) -6 × 10
-4
   (d) zero 
Q 4.  In a process the pressure of a gas remains constant. If the temperature is doubled, then the change 
in the volume will be  
  (a) 100%   (b) 200%   (c) 50%   (d) 25% 
Q 5.  The average kinetic energy of the molecules of an ideal gas at 10°C has the value E. The 
temperature at which the kinetic energy of the same gas becomes 2E is 
  (a) 5°C   (b) 10°C  (c) 40°C   (d) None of these 
Q 6.  A polyatomic gas with n degrees of freedom has a mean energy per molecule given by 
 (a) 
n
RT
2
   (b) 
1
RT
2
   (c) 
n
kT
2
   (d) 
1
kT
2
 
Q 7.  The temperature of an ideal gas is increased from 27°C to 927°C. The rms speed of its molecules 
becomes 
  (a) twice   (b) half   (c) four times   (d) one-fourth 
Q 8.  In case of hydrogen and oxygen at NTP, which of the following is the same for both?  
  (a) Average linear momentum per molecule (b) Average KE per molecule 
  (c) KE per unit volume    (d) KE per unit mass 
Q 9.  Two thermally insulated vessels 1 and 2 are filled with air at temperatures (T1, T2 ), volumes (V1, 
V2) and pressures (P1, P2) respectively. If the valve joining the two vessels is opened, the 
temperature inside the vessel at equilibrium will be (P = common pressure) 
  (a) T1 + T2   (b) (T1 +T2)/2  (c) 
1 2 1 2
1 1 2 2 2 1
T T P(V V )
P V T P V T
?
?
  (d) 
1 2 1 1 2 2
1 1 2 2 2 1
T T (P V P V )
P VT P V T
?
?
 
Q 10.  Two marks on a glass rod 10 cm apart are found to increase their distance by 0.08 mm when the 
rod is heated from 0°C to 100°C. A flask made of the same glass as that of rod measures a volume 
of 100 cc at 0°C. The volume it measures at 100°C in cc is 
  (a) 100.24   (b) 100.12  (c) 100.36   (d) 100.48 
Q 11.  The given curve represents the variation of temperature as a function of volume for one mole of an 
ideal gas. Which of the following curves best represents the variation of pressure as a function of 
volume? 
 
  (a)   (b)   (c)   (d) 
Q 12.  A gas is found to obey the law P V = constant. The initial temperature and volume are T0 and V0. 
If the gas
 
expands to a volume 3 V0, then the final temperature becomes 
 (a) 
0
3T   (b) 
0
2T   (c) 
0
T
3
   (d) 
0
T
2
 
Q 13.  Air fills a room in winter at 7°C and in summer at 37°C. If the pressure is the same in winter and 
summer, the ratio of the weight of the air filled in winter and that in summer is 
  (a) 2.2    (b) 1.75   (c) 1.1    (d) 3.3 
Q 14.  Three closed vessels A, B and C are at the same temperature T and contain gases which obey 
Maxwell distribution law of velocities. Vessels contains O2, B only N2 and C mixture of equal 
quantities of O2 and N2. If the average speed of the O2 molecules in vessel A is v 1 that of N2 
molecules in vessel B is v2, then the average speed of the O2 molecules in vessel C is 
  (a) 
12
(v v )
2
?
   (b) v1    (c) 
12
vv   (d) None of these 
Q 15.  In a very good vacuum system in the laboratory, the vacuum attained was 10
-13
 atm. If the 
temperature of the system was 300 K, the number of molecules present in a volume of 1 cm is 
  (a) 2.4 × 10
6  
(b) 24   (c) 2.4 × 10
9
   (d) zero 
Q 16.  If nitrogen gas molecule goes straight up with its rms speed at 0°C from the surface of the earth 
and there are no collisions with other molecules, then it will rise to an approximate height of 
  (a) 8 km   (b) 12 km   (c) 12 m   (d) 8 m 
Q 17.  The coefficient of linear expansion of steel and brass are 11 × 10
-6
/°C and 19 × 10
-6
/°C 
respectively. If their difference in lengths at all temperatures has to kept constant at 30 cm, their 
lengths at 0°C should be  
  (a) 71.25 cm and 41.25 cm    (b) 82 cm and 52 cm 
  (c) 92 cm and 62 cm     (d) 62.25 cm and 32.25 cm 
Q 18.  The given P-U graph shows the variation of internal energy of an ideal gas with increase in 
pressure. Which of the following pressure-volume graph is equivalent to this graph? 
 
  (a) (b)   (c) (d) 
Q 19.  The expansion of an ideal gas of mass m at a constant pressure P is given by the straight line B. 
Then, the expansion of the same ideal gas of mass 2m at a pressure 2P is given by the straight line 
 
  (a) C   (b) A   (c) B   (d) data insufficient
 
 
Q 20.  28 g of N2 gas is contained in a flask at a pressure of 10 atm and at a temperature of 57° C. It is 
round that due to leakage in the flask, the pressure is reduced to half and the temperature to 27°C. 
The quantity of N2 gas that leaked out is 
  (a) 11/20 g   (b) 20/11g   (c) 5/63 g   (d) 63/5 g 
Q 21.  A mixture of 4g of hydrogen and 8 g of helium at NTP has a density about 
  (a) 0.22 kg/m
3
  (b) 0.62 kg/m
3
  (c) 1.12 kg/m
3
  (d) 0.13 kg/m
3
 
Q 22.  The pressure (P) and the density ( ?) of given mass of a gas expressed by Boyle's law, P = K ? 
holds true  
  (a) for any gas under any condition   (b) for some gases under any conditions 
  (c) only if the temperature is kept constant  (d) None of these 
  More than One Correct Options 
Q 23.  During an experiment, an ideal gas is found to obey a condition 
2
P
?
= constant, ( ?
 
= density of the 
gas). 
The gas is initially at temperature T, pressure P and density ?. The gas expands such that density 
changes to ?/2. 
  (a) The pressure of the gas changes to 2P
 
(b) The temperature of the gas changes to 2T 
  (c) The graph of the above process on P-T diagram is parabola 
  (d) The graph of the above process on P-T diagram is hyperbola 
Q 24.  During an experiment, an ideal gas is found to obey a condition VP
2
 = constant. The gas is 
initially at a temperature T, pressure P and volume V. The gas expands to volume 4V. 
Page 4


For JEE Advanced 
Objective Questions 
  Single Correct Option 
Q 1.  The average velocity of molecules of a gas of molecular weight M at temperature T is 
 (a) 
3RT
M
   (b) 
8RT
M ?
   (c) 
2RT
M
   (d) zero 
Q 2.  Four particles have velocities 1,0,2 and 3 m/s. The root mean square velocity of the particles 
(definition wise) is 
  (a) 3.5 m/s   (b) 3.5 m / s   (c) 1.5m/s   (d) 
14
m / s
3
 
Q 3.  A steel rod of length 1 m is heated from 25° to 75°C keeping its length constant. The longitudinal 
strain developed in the rod is (Given coefficient of linear expansion of steel = 12 × 10
-6
/°C) 
  (a) 6 × 10
-4
   (b) -6 × 10
-5
   (c) -6 × 10
-4
   (d) zero 
Q 4.  In a process the pressure of a gas remains constant. If the temperature is doubled, then the change 
in the volume will be  
  (a) 100%   (b) 200%   (c) 50%   (d) 25% 
Q 5.  The average kinetic energy of the molecules of an ideal gas at 10°C has the value E. The 
temperature at which the kinetic energy of the same gas becomes 2E is 
  (a) 5°C   (b) 10°C  (c) 40°C   (d) None of these 
Q 6.  A polyatomic gas with n degrees of freedom has a mean energy per molecule given by 
 (a) 
n
RT
2
   (b) 
1
RT
2
   (c) 
n
kT
2
   (d) 
1
kT
2
 
Q 7.  The temperature of an ideal gas is increased from 27°C to 927°C. The rms speed of its molecules 
becomes 
  (a) twice   (b) half   (c) four times   (d) one-fourth 
Q 8.  In case of hydrogen and oxygen at NTP, which of the following is the same for both?  
  (a) Average linear momentum per molecule (b) Average KE per molecule 
  (c) KE per unit volume    (d) KE per unit mass 
Q 9.  Two thermally insulated vessels 1 and 2 are filled with air at temperatures (T1, T2 ), volumes (V1, 
V2) and pressures (P1, P2) respectively. If the valve joining the two vessels is opened, the 
temperature inside the vessel at equilibrium will be (P = common pressure) 
  (a) T1 + T2   (b) (T1 +T2)/2  (c) 
1 2 1 2
1 1 2 2 2 1
T T P(V V )
P V T P V T
?
?
  (d) 
1 2 1 1 2 2
1 1 2 2 2 1
T T (P V P V )
P VT P V T
?
?
 
Q 10.  Two marks on a glass rod 10 cm apart are found to increase their distance by 0.08 mm when the 
rod is heated from 0°C to 100°C. A flask made of the same glass as that of rod measures a volume 
of 100 cc at 0°C. The volume it measures at 100°C in cc is 
  (a) 100.24   (b) 100.12  (c) 100.36   (d) 100.48 
Q 11.  The given curve represents the variation of temperature as a function of volume for one mole of an 
ideal gas. Which of the following curves best represents the variation of pressure as a function of 
volume? 
 
  (a)   (b)   (c)   (d) 
Q 12.  A gas is found to obey the law P V = constant. The initial temperature and volume are T0 and V0. 
If the gas
 
expands to a volume 3 V0, then the final temperature becomes 
 (a) 
0
3T   (b) 
0
2T   (c) 
0
T
3
   (d) 
0
T
2
 
Q 13.  Air fills a room in winter at 7°C and in summer at 37°C. If the pressure is the same in winter and 
summer, the ratio of the weight of the air filled in winter and that in summer is 
  (a) 2.2    (b) 1.75   (c) 1.1    (d) 3.3 
Q 14.  Three closed vessels A, B and C are at the same temperature T and contain gases which obey 
Maxwell distribution law of velocities. Vessels contains O2, B only N2 and C mixture of equal 
quantities of O2 and N2. If the average speed of the O2 molecules in vessel A is v 1 that of N2 
molecules in vessel B is v2, then the average speed of the O2 molecules in vessel C is 
  (a) 
12
(v v )
2
?
   (b) v1    (c) 
12
vv   (d) None of these 
Q 15.  In a very good vacuum system in the laboratory, the vacuum attained was 10
-13
 atm. If the 
temperature of the system was 300 K, the number of molecules present in a volume of 1 cm is 
  (a) 2.4 × 10
6  
(b) 24   (c) 2.4 × 10
9
   (d) zero 
Q 16.  If nitrogen gas molecule goes straight up with its rms speed at 0°C from the surface of the earth 
and there are no collisions with other molecules, then it will rise to an approximate height of 
  (a) 8 km   (b) 12 km   (c) 12 m   (d) 8 m 
Q 17.  The coefficient of linear expansion of steel and brass are 11 × 10
-6
/°C and 19 × 10
-6
/°C 
respectively. If their difference in lengths at all temperatures has to kept constant at 30 cm, their 
lengths at 0°C should be  
  (a) 71.25 cm and 41.25 cm    (b) 82 cm and 52 cm 
  (c) 92 cm and 62 cm     (d) 62.25 cm and 32.25 cm 
Q 18.  The given P-U graph shows the variation of internal energy of an ideal gas with increase in 
pressure. Which of the following pressure-volume graph is equivalent to this graph? 
 
  (a) (b)   (c) (d) 
Q 19.  The expansion of an ideal gas of mass m at a constant pressure P is given by the straight line B. 
Then, the expansion of the same ideal gas of mass 2m at a pressure 2P is given by the straight line 
 
  (a) C   (b) A   (c) B   (d) data insufficient
 
 
Q 20.  28 g of N2 gas is contained in a flask at a pressure of 10 atm and at a temperature of 57° C. It is 
round that due to leakage in the flask, the pressure is reduced to half and the temperature to 27°C. 
The quantity of N2 gas that leaked out is 
  (a) 11/20 g   (b) 20/11g   (c) 5/63 g   (d) 63/5 g 
Q 21.  A mixture of 4g of hydrogen and 8 g of helium at NTP has a density about 
  (a) 0.22 kg/m
3
  (b) 0.62 kg/m
3
  (c) 1.12 kg/m
3
  (d) 0.13 kg/m
3
 
Q 22.  The pressure (P) and the density ( ?) of given mass of a gas expressed by Boyle's law, P = K ? 
holds true  
  (a) for any gas under any condition   (b) for some gases under any conditions 
  (c) only if the temperature is kept constant  (d) None of these 
  More than One Correct Options 
Q 23.  During an experiment, an ideal gas is found to obey a condition 
2
P
?
= constant, ( ?
 
= density of the 
gas). 
The gas is initially at temperature T, pressure P and density ?. The gas expands such that density 
changes to ?/2. 
  (a) The pressure of the gas changes to 2P
 
(b) The temperature of the gas changes to 2T 
  (c) The graph of the above process on P-T diagram is parabola 
  (d) The graph of the above process on P-T diagram is hyperbola 
Q 24.  During an experiment, an ideal gas is found to obey a condition VP
2
 = constant. The gas is 
initially at a temperature T, pressure P and volume V. The gas expands to volume 4V. 
  (a) The pressure of gas changes to 
P
2
  (b) The temperature of gas changes to 4T 
  (c) The graph of the above process on P-T diagram is parabola 
  (d) The graph of the above process on P-T diagram is hyperbola 
Q 25.  Find the correct options 
  (a) Ice point in Fahrenheit scale is 32°F  (b) Ice point in Fahrenheit scale is 98.8°F 
  (c) Steam point in Fahrenheit scale is 212°F  (d) Steam point in Fahrenheit scale is 252°F 
Q 26.  In the P- F diagram shown in figure, choose the correct options for the process a-b : 
 
  (a) density of gas has reduced to half 
  (b) temperature of gas has increased to two times 
  (c) internal energy of gas has increased to four times 
  (d) T-V graph is a parabola passing through origin 
Q 27.  Choose the wrong options 
  (a) Translational kinetic energy of all ideal gases at same temperature is same 
  (b) In one degree of freedom all ideal gases has internal energy 
1
RT
2
? 
  (c) Translational degree of freedom of all ideal gases is three  
  (d) Translational kinetic energy of one mole of all ideal gases is 
3
RT
2
 
Q 28.  Along the line-1, mass of gas is m l and pressure is P1. Along the line-2 mass of same gas is m 2 and 
pressure is P2. Choose the correct options. 
 
  (a) m 1 may be less than m 2   (b) m 2 may be less than m 1 
  (c) P1 may be less than P2   (d) P2 may be less than P1  
Q 29.  Choose the correct options 
  (a) In 
m
P RT
M
? , m is mass of gas per unit volume 
  (b) In 
m
PV RT
M
? , m is mass of one molecule of gas 
  (c) In 
2
rms
1 mN
Pv
3V
? , m is total mass of gas. 
Page 5


For JEE Advanced 
Objective Questions 
  Single Correct Option 
Q 1.  The average velocity of molecules of a gas of molecular weight M at temperature T is 
 (a) 
3RT
M
   (b) 
8RT
M ?
   (c) 
2RT
M
   (d) zero 
Q 2.  Four particles have velocities 1,0,2 and 3 m/s. The root mean square velocity of the particles 
(definition wise) is 
  (a) 3.5 m/s   (b) 3.5 m / s   (c) 1.5m/s   (d) 
14
m / s
3
 
Q 3.  A steel rod of length 1 m is heated from 25° to 75°C keeping its length constant. The longitudinal 
strain developed in the rod is (Given coefficient of linear expansion of steel = 12 × 10
-6
/°C) 
  (a) 6 × 10
-4
   (b) -6 × 10
-5
   (c) -6 × 10
-4
   (d) zero 
Q 4.  In a process the pressure of a gas remains constant. If the temperature is doubled, then the change 
in the volume will be  
  (a) 100%   (b) 200%   (c) 50%   (d) 25% 
Q 5.  The average kinetic energy of the molecules of an ideal gas at 10°C has the value E. The 
temperature at which the kinetic energy of the same gas becomes 2E is 
  (a) 5°C   (b) 10°C  (c) 40°C   (d) None of these 
Q 6.  A polyatomic gas with n degrees of freedom has a mean energy per molecule given by 
 (a) 
n
RT
2
   (b) 
1
RT
2
   (c) 
n
kT
2
   (d) 
1
kT
2
 
Q 7.  The temperature of an ideal gas is increased from 27°C to 927°C. The rms speed of its molecules 
becomes 
  (a) twice   (b) half   (c) four times   (d) one-fourth 
Q 8.  In case of hydrogen and oxygen at NTP, which of the following is the same for both?  
  (a) Average linear momentum per molecule (b) Average KE per molecule 
  (c) KE per unit volume    (d) KE per unit mass 
Q 9.  Two thermally insulated vessels 1 and 2 are filled with air at temperatures (T1, T2 ), volumes (V1, 
V2) and pressures (P1, P2) respectively. If the valve joining the two vessels is opened, the 
temperature inside the vessel at equilibrium will be (P = common pressure) 
  (a) T1 + T2   (b) (T1 +T2)/2  (c) 
1 2 1 2
1 1 2 2 2 1
T T P(V V )
P V T P V T
?
?
  (d) 
1 2 1 1 2 2
1 1 2 2 2 1
T T (P V P V )
P VT P V T
?
?
 
Q 10.  Two marks on a glass rod 10 cm apart are found to increase their distance by 0.08 mm when the 
rod is heated from 0°C to 100°C. A flask made of the same glass as that of rod measures a volume 
of 100 cc at 0°C. The volume it measures at 100°C in cc is 
  (a) 100.24   (b) 100.12  (c) 100.36   (d) 100.48 
Q 11.  The given curve represents the variation of temperature as a function of volume for one mole of an 
ideal gas. Which of the following curves best represents the variation of pressure as a function of 
volume? 
 
  (a)   (b)   (c)   (d) 
Q 12.  A gas is found to obey the law P V = constant. The initial temperature and volume are T0 and V0. 
If the gas
 
expands to a volume 3 V0, then the final temperature becomes 
 (a) 
0
3T   (b) 
0
2T   (c) 
0
T
3
   (d) 
0
T
2
 
Q 13.  Air fills a room in winter at 7°C and in summer at 37°C. If the pressure is the same in winter and 
summer, the ratio of the weight of the air filled in winter and that in summer is 
  (a) 2.2    (b) 1.75   (c) 1.1    (d) 3.3 
Q 14.  Three closed vessels A, B and C are at the same temperature T and contain gases which obey 
Maxwell distribution law of velocities. Vessels contains O2, B only N2 and C mixture of equal 
quantities of O2 and N2. If the average speed of the O2 molecules in vessel A is v 1 that of N2 
molecules in vessel B is v2, then the average speed of the O2 molecules in vessel C is 
  (a) 
12
(v v )
2
?
   (b) v1    (c) 
12
vv   (d) None of these 
Q 15.  In a very good vacuum system in the laboratory, the vacuum attained was 10
-13
 atm. If the 
temperature of the system was 300 K, the number of molecules present in a volume of 1 cm is 
  (a) 2.4 × 10
6  
(b) 24   (c) 2.4 × 10
9
   (d) zero 
Q 16.  If nitrogen gas molecule goes straight up with its rms speed at 0°C from the surface of the earth 
and there are no collisions with other molecules, then it will rise to an approximate height of 
  (a) 8 km   (b) 12 km   (c) 12 m   (d) 8 m 
Q 17.  The coefficient of linear expansion of steel and brass are 11 × 10
-6
/°C and 19 × 10
-6
/°C 
respectively. If their difference in lengths at all temperatures has to kept constant at 30 cm, their 
lengths at 0°C should be  
  (a) 71.25 cm and 41.25 cm    (b) 82 cm and 52 cm 
  (c) 92 cm and 62 cm     (d) 62.25 cm and 32.25 cm 
Q 18.  The given P-U graph shows the variation of internal energy of an ideal gas with increase in 
pressure. Which of the following pressure-volume graph is equivalent to this graph? 
 
  (a) (b)   (c) (d) 
Q 19.  The expansion of an ideal gas of mass m at a constant pressure P is given by the straight line B. 
Then, the expansion of the same ideal gas of mass 2m at a pressure 2P is given by the straight line 
 
  (a) C   (b) A   (c) B   (d) data insufficient
 
 
Q 20.  28 g of N2 gas is contained in a flask at a pressure of 10 atm and at a temperature of 57° C. It is 
round that due to leakage in the flask, the pressure is reduced to half and the temperature to 27°C. 
The quantity of N2 gas that leaked out is 
  (a) 11/20 g   (b) 20/11g   (c) 5/63 g   (d) 63/5 g 
Q 21.  A mixture of 4g of hydrogen and 8 g of helium at NTP has a density about 
  (a) 0.22 kg/m
3
  (b) 0.62 kg/m
3
  (c) 1.12 kg/m
3
  (d) 0.13 kg/m
3
 
Q 22.  The pressure (P) and the density ( ?) of given mass of a gas expressed by Boyle's law, P = K ? 
holds true  
  (a) for any gas under any condition   (b) for some gases under any conditions 
  (c) only if the temperature is kept constant  (d) None of these 
  More than One Correct Options 
Q 23.  During an experiment, an ideal gas is found to obey a condition 
2
P
?
= constant, ( ?
 
= density of the 
gas). 
The gas is initially at temperature T, pressure P and density ?. The gas expands such that density 
changes to ?/2. 
  (a) The pressure of the gas changes to 2P
 
(b) The temperature of the gas changes to 2T 
  (c) The graph of the above process on P-T diagram is parabola 
  (d) The graph of the above process on P-T diagram is hyperbola 
Q 24.  During an experiment, an ideal gas is found to obey a condition VP
2
 = constant. The gas is 
initially at a temperature T, pressure P and volume V. The gas expands to volume 4V. 
  (a) The pressure of gas changes to 
P
2
  (b) The temperature of gas changes to 4T 
  (c) The graph of the above process on P-T diagram is parabola 
  (d) The graph of the above process on P-T diagram is hyperbola 
Q 25.  Find the correct options 
  (a) Ice point in Fahrenheit scale is 32°F  (b) Ice point in Fahrenheit scale is 98.8°F 
  (c) Steam point in Fahrenheit scale is 212°F  (d) Steam point in Fahrenheit scale is 252°F 
Q 26.  In the P- F diagram shown in figure, choose the correct options for the process a-b : 
 
  (a) density of gas has reduced to half 
  (b) temperature of gas has increased to two times 
  (c) internal energy of gas has increased to four times 
  (d) T-V graph is a parabola passing through origin 
Q 27.  Choose the wrong options 
  (a) Translational kinetic energy of all ideal gases at same temperature is same 
  (b) In one degree of freedom all ideal gases has internal energy 
1
RT
2
? 
  (c) Translational degree of freedom of all ideal gases is three  
  (d) Translational kinetic energy of one mole of all ideal gases is 
3
RT
2
 
Q 28.  Along the line-1, mass of gas is m l and pressure is P1. Along the line-2 mass of same gas is m 2 and 
pressure is P2. Choose the correct options. 
 
  (a) m 1 may be less than m 2   (b) m 2 may be less than m 1 
  (c) P1 may be less than P2   (d) P2 may be less than P1  
Q 29.  Choose the correct options 
  (a) In 
m
P RT
M
? , m is mass of gas per unit volume 
  (b) In 
m
PV RT
M
? , m is mass of one molecule of gas 
  (c) In 
2
rms
1 mN
Pv
3V
? , m is total mass of gas. 
  (d) In 
rms
3kT
v
m
? , m is mass of one molecule of gas 
Answers 
  1.(b) 2.(b) 3.(c) 4.(a) 5.(d) 6.(c) 7.(a) 8.(b) 9.(c) 10, (a) 11.(a) 12. (a) 13.(c) 14. (b) 15.(a) 16. (b) 
  17. (a) 18.(b) 19. (c) 20. (d) 21.(d) 22.(c) 
  More than One Correct Options 
  23. (b,d) 24. (a,d) 25. (a,c) 26. (a,c,d) 27. (a,b) 28. (a,b,c,d) 29. (a,d) 
Solutions 
1.  No required. 
2.  
3.  It means rod is compressed from its natural length by ?l  
   
   = -6 × 10
-4
 
4.  If P = constant, then V ? T 
5. E ? T 
   
  ?   T2 = 2T1 = 2 (273+ 10)= 566 K = 293°C 
6.  Not required. 
7.  T1 = 273 + 27 = 300 K 
  T2 = 273+ 927 = 1200K 
   v rms ? T 
  T has becomes four times. Therefore vrms will become two times. 
8.  Hydrogen and oxygen both are diatomic gases. Therefore, average kinetic energy per molecule is 
    (as f = 5) 
9.  (n1 + n2)i = (n1 + n 2)f 
   
  Solving we get, 
10. ?l = l ? ? ? 
   
   = 0.24 cc