Thermometry, Thermal Expansion & Kinetic Theory of Gases (Part - 2) - Physics, Solution by DC Pandey NEET Notes | EduRev

DC Pandey (Questions & Solutions) of Physics: NEET

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NEET : Thermometry, Thermal Expansion & Kinetic Theory of Gases (Part - 2) - Physics, Solution by DC Pandey NEET Notes | EduRev

 Page 1


Introductory Exercise 17.2 
Q 1.  From the graph for an ideal gas state whether m
1
 or m
2
 is greater? 
 
Q 2.  A vessel is filled with an ideal gas at a pressure of 20 atm and is at a temperature of 27°C. One-
half of the mass is removed from the vessel and the temperature of the remaining gas is increased 
to 87°C. At this temperature find the pressure of the gas. 
Q 3.  A vessel contains a mixture of 7 g of nitrogen and 11 g of carbondioxide at temperature T = 290K. 
If pressure of the mixture is 1 atm (=1.01 × 10
5
 N/m
2
), calculate its density (R = 8.31 J/mol-K). 
Q 4.  An electric bulb of volume 250 cm
3
 was sealed off during manufacture at a pressure of 10
-3
 mm of 
mercury at 27°C. Compute the number of air molecules contained in the bulb. Given that R = 8.31 
J/mol -K and N
A
 = 6.02 × 10
23
 per mol. 
Q 5.  State whether P
1
 > P
2
 or P
2
 > P
1
 for given mass of a gas? 
 
Q 6.  For a given mass of a gas what is the shape of P versus 
1
V
graph at constant temperature?  
Solutions 
1.  
   
  At constant volume T -P graph is a straight line of slope, 
  Slope of m
1
 is less. Hence m
1
 is greater. 
2.  
   
3.   n
1
 = number of moles of nitrogen n
2
 = number of moles of CO
2
 = 
   
   
4.  PV = nRT 
Page 2


Introductory Exercise 17.2 
Q 1.  From the graph for an ideal gas state whether m
1
 or m
2
 is greater? 
 
Q 2.  A vessel is filled with an ideal gas at a pressure of 20 atm and is at a temperature of 27°C. One-
half of the mass is removed from the vessel and the temperature of the remaining gas is increased 
to 87°C. At this temperature find the pressure of the gas. 
Q 3.  A vessel contains a mixture of 7 g of nitrogen and 11 g of carbondioxide at temperature T = 290K. 
If pressure of the mixture is 1 atm (=1.01 × 10
5
 N/m
2
), calculate its density (R = 8.31 J/mol-K). 
Q 4.  An electric bulb of volume 250 cm
3
 was sealed off during manufacture at a pressure of 10
-3
 mm of 
mercury at 27°C. Compute the number of air molecules contained in the bulb. Given that R = 8.31 
J/mol -K and N
A
 = 6.02 × 10
23
 per mol. 
Q 5.  State whether P
1
 > P
2
 or P
2
 > P
1
 for given mass of a gas? 
 
Q 6.  For a given mass of a gas what is the shape of P versus 
1
V
graph at constant temperature?  
Solutions 
1.  
   
  At constant volume T -P graph is a straight line of slope, 
  Slope of m
1
 is less. Hence m
1
 is greater. 
2.  
   
3.   n
1
 = number of moles of nitrogen n
2
 = number of moles of CO
2
 = 
   
   
4.  PV = nRT 
   
    
   = 1.33 × 10
-8
 
  ?  Number of molecular = (n)  
   N
A 
= (1.33 × 10
-8
) (6.02 × 10
23
) = 8 × 10
15
 
 5.    
  For given mass, V-T graph is a straight line passing through origin having 
    
  Slope of P
2
 is more. Hence P
2
< P
1
. 
6.  
  i.e., P versus 
1
V
graph is a straight line passing through origin of slope nRT. 
 
Introductory Exercise 17.3 
Q 1.  The average speed of all the molecules in a gas at a given instant is not zero, whereas the average 
velocity of all the molecules is zero. Explain why? 
Q 2.  A sample of helium gas is at a temperature of 300 K and a pressure of 0.5 atm. What is the 
average kinetic energy of a molecule of a gas? 
Q 3.  A sample of helium and neon gases has a temperature of 300 K and pressure of 1.0 atm. The molar 
mass of helium is 4.0 g/mol and that of neon is 20.2 g/mol. 
  (a) Find the rms speed of the helium atoms and of the neon atoms. 
  (b) What is the average kinetic energy per atom of each gas?  
Q 4.  At what temperature will the particles in a sample of helium gas have an rms speed of 1.0 km/s? 
Q 5.  At 0°C and 1.0 atm (=1.01 × 10
5
 N/m
2
) pressure the densities of air, oxygen and nitrogen are 
1.284 kg/m
3
, 1.429 kg/m
3
 and 1.251 kg/m
3
 respectively. Calculate the percentage of nitrogen in 
the air from these data, assuming only these two gases to be present. 
Q 6.  An air bubble of 20 cm
3
 volume is at the bottom of a lake 40 meters deep where the temperature is 
4°C. The bubble rises to the surface which is at a temperature of 20°C. Take the temperature to be 
the same as that of the surrounding water and find its volume just before it reaches the surface. 
Q 7.  If the water molecules in 1.0 g of water were distributed uniformly over the surface of earth, how 
many such molecules would there be in 1.0 cm
2
 of earth's surface? 
Q 8.  For a certain gas the heat capacity at constant pressure is greater than that at constant volume by 
29.1J/K. 
  (a) How many moles of the gas are there? 
  (b) If the gas is monoatomic, what are heat capacities at constant volume and pressure ? 
Page 3


Introductory Exercise 17.2 
Q 1.  From the graph for an ideal gas state whether m
1
 or m
2
 is greater? 
 
Q 2.  A vessel is filled with an ideal gas at a pressure of 20 atm and is at a temperature of 27°C. One-
half of the mass is removed from the vessel and the temperature of the remaining gas is increased 
to 87°C. At this temperature find the pressure of the gas. 
Q 3.  A vessel contains a mixture of 7 g of nitrogen and 11 g of carbondioxide at temperature T = 290K. 
If pressure of the mixture is 1 atm (=1.01 × 10
5
 N/m
2
), calculate its density (R = 8.31 J/mol-K). 
Q 4.  An electric bulb of volume 250 cm
3
 was sealed off during manufacture at a pressure of 10
-3
 mm of 
mercury at 27°C. Compute the number of air molecules contained in the bulb. Given that R = 8.31 
J/mol -K and N
A
 = 6.02 × 10
23
 per mol. 
Q 5.  State whether P
1
 > P
2
 or P
2
 > P
1
 for given mass of a gas? 
 
Q 6.  For a given mass of a gas what is the shape of P versus 
1
V
graph at constant temperature?  
Solutions 
1.  
   
  At constant volume T -P graph is a straight line of slope, 
  Slope of m
1
 is less. Hence m
1
 is greater. 
2.  
   
3.   n
1
 = number of moles of nitrogen n
2
 = number of moles of CO
2
 = 
   
   
4.  PV = nRT 
   
    
   = 1.33 × 10
-8
 
  ?  Number of molecular = (n)  
   N
A 
= (1.33 × 10
-8
) (6.02 × 10
23
) = 8 × 10
15
 
 5.    
  For given mass, V-T graph is a straight line passing through origin having 
    
  Slope of P
2
 is more. Hence P
2
< P
1
. 
6.  
  i.e., P versus 
1
V
graph is a straight line passing through origin of slope nRT. 
 
Introductory Exercise 17.3 
Q 1.  The average speed of all the molecules in a gas at a given instant is not zero, whereas the average 
velocity of all the molecules is zero. Explain why? 
Q 2.  A sample of helium gas is at a temperature of 300 K and a pressure of 0.5 atm. What is the 
average kinetic energy of a molecule of a gas? 
Q 3.  A sample of helium and neon gases has a temperature of 300 K and pressure of 1.0 atm. The molar 
mass of helium is 4.0 g/mol and that of neon is 20.2 g/mol. 
  (a) Find the rms speed of the helium atoms and of the neon atoms. 
  (b) What is the average kinetic energy per atom of each gas?  
Q 4.  At what temperature will the particles in a sample of helium gas have an rms speed of 1.0 km/s? 
Q 5.  At 0°C and 1.0 atm (=1.01 × 10
5
 N/m
2
) pressure the densities of air, oxygen and nitrogen are 
1.284 kg/m
3
, 1.429 kg/m
3
 and 1.251 kg/m
3
 respectively. Calculate the percentage of nitrogen in 
the air from these data, assuming only these two gases to be present. 
Q 6.  An air bubble of 20 cm
3
 volume is at the bottom of a lake 40 meters deep where the temperature is 
4°C. The bubble rises to the surface which is at a temperature of 20°C. Take the temperature to be 
the same as that of the surrounding water and find its volume just before it reaches the surface. 
Q 7.  If the water molecules in 1.0 g of water were distributed uniformly over the surface of earth, how 
many such molecules would there be in 1.0 cm
2
 of earth's surface? 
Q 8.  For a certain gas the heat capacity at constant pressure is greater than that at constant volume by 
29.1J/K. 
  (a) How many moles of the gas are there? 
  (b) If the gas is monoatomic, what are heat capacities at constant volume and pressure ? 
(c) If the gas molecules are diatomic which rotate but do not vibrate, what are heat capacities at 
constant volume and at constant pressure. 
Q 9.  The heat capacity at constant volume of a sample of a monoatomic gas is 35 J/K. Find : 
  (a) the number of moles  (b) the internal energy at 0°C 
  (c) the molor heat capacity at constant pressure. 
Q 10.  For any distribution of speeds v
rms
 ? v
av
.
 
Is this statement true or false? 
Solutions 
1.  See the answer 
2.  Helium gas is monoatomic. So its degree of freedom f = 3. Average kinetic energy of 1 molecule 
of gas 
    
    
   = 6.21 × 10
-21 
J 
3.  (a) 
  For He gas : 
   = 1368 m/s 
  For Ne gas : 
   = 609 m/s 
  (b) Each gas is monotonic for which degree of freedom f = 3. Hence average kinetic energy of one 
atom 
    
   = 6.21 × 10
-21
 J 
4.   
   
5.  Let mass of nitrogen = (m) g. Then mass of oxygen = (100 - m) g. Number of moles of nitrogen, 
    and number of moles of oxygen 
    
  For air 
    
Page 4


Introductory Exercise 17.2 
Q 1.  From the graph for an ideal gas state whether m
1
 or m
2
 is greater? 
 
Q 2.  A vessel is filled with an ideal gas at a pressure of 20 atm and is at a temperature of 27°C. One-
half of the mass is removed from the vessel and the temperature of the remaining gas is increased 
to 87°C. At this temperature find the pressure of the gas. 
Q 3.  A vessel contains a mixture of 7 g of nitrogen and 11 g of carbondioxide at temperature T = 290K. 
If pressure of the mixture is 1 atm (=1.01 × 10
5
 N/m
2
), calculate its density (R = 8.31 J/mol-K). 
Q 4.  An electric bulb of volume 250 cm
3
 was sealed off during manufacture at a pressure of 10
-3
 mm of 
mercury at 27°C. Compute the number of air molecules contained in the bulb. Given that R = 8.31 
J/mol -K and N
A
 = 6.02 × 10
23
 per mol. 
Q 5.  State whether P
1
 > P
2
 or P
2
 > P
1
 for given mass of a gas? 
 
Q 6.  For a given mass of a gas what is the shape of P versus 
1
V
graph at constant temperature?  
Solutions 
1.  
   
  At constant volume T -P graph is a straight line of slope, 
  Slope of m
1
 is less. Hence m
1
 is greater. 
2.  
   
3.   n
1
 = number of moles of nitrogen n
2
 = number of moles of CO
2
 = 
   
   
4.  PV = nRT 
   
    
   = 1.33 × 10
-8
 
  ?  Number of molecular = (n)  
   N
A 
= (1.33 × 10
-8
) (6.02 × 10
23
) = 8 × 10
15
 
 5.    
  For given mass, V-T graph is a straight line passing through origin having 
    
  Slope of P
2
 is more. Hence P
2
< P
1
. 
6.  
  i.e., P versus 
1
V
graph is a straight line passing through origin of slope nRT. 
 
Introductory Exercise 17.3 
Q 1.  The average speed of all the molecules in a gas at a given instant is not zero, whereas the average 
velocity of all the molecules is zero. Explain why? 
Q 2.  A sample of helium gas is at a temperature of 300 K and a pressure of 0.5 atm. What is the 
average kinetic energy of a molecule of a gas? 
Q 3.  A sample of helium and neon gases has a temperature of 300 K and pressure of 1.0 atm. The molar 
mass of helium is 4.0 g/mol and that of neon is 20.2 g/mol. 
  (a) Find the rms speed of the helium atoms and of the neon atoms. 
  (b) What is the average kinetic energy per atom of each gas?  
Q 4.  At what temperature will the particles in a sample of helium gas have an rms speed of 1.0 km/s? 
Q 5.  At 0°C and 1.0 atm (=1.01 × 10
5
 N/m
2
) pressure the densities of air, oxygen and nitrogen are 
1.284 kg/m
3
, 1.429 kg/m
3
 and 1.251 kg/m
3
 respectively. Calculate the percentage of nitrogen in 
the air from these data, assuming only these two gases to be present. 
Q 6.  An air bubble of 20 cm
3
 volume is at the bottom of a lake 40 meters deep where the temperature is 
4°C. The bubble rises to the surface which is at a temperature of 20°C. Take the temperature to be 
the same as that of the surrounding water and find its volume just before it reaches the surface. 
Q 7.  If the water molecules in 1.0 g of water were distributed uniformly over the surface of earth, how 
many such molecules would there be in 1.0 cm
2
 of earth's surface? 
Q 8.  For a certain gas the heat capacity at constant pressure is greater than that at constant volume by 
29.1J/K. 
  (a) How many moles of the gas are there? 
  (b) If the gas is monoatomic, what are heat capacities at constant volume and pressure ? 
(c) If the gas molecules are diatomic which rotate but do not vibrate, what are heat capacities at 
constant volume and at constant pressure. 
Q 9.  The heat capacity at constant volume of a sample of a monoatomic gas is 35 J/K. Find : 
  (a) the number of moles  (b) the internal energy at 0°C 
  (c) the molor heat capacity at constant pressure. 
Q 10.  For any distribution of speeds v
rms
 ? v
av
.
 
Is this statement true or false? 
Solutions 
1.  See the answer 
2.  Helium gas is monoatomic. So its degree of freedom f = 3. Average kinetic energy of 1 molecule 
of gas 
    
    
   = 6.21 × 10
-21 
J 
3.  (a) 
  For He gas : 
   = 1368 m/s 
  For Ne gas : 
   = 609 m/s 
  (b) Each gas is monotonic for which degree of freedom f = 3. Hence average kinetic energy of one 
atom 
    
   = 6.21 × 10
-21
 J 
4.   
   
5.  Let mass of nitrogen = (m) g. Then mass of oxygen = (100 - m) g. Number of moles of nitrogen, 
    and number of moles of oxygen 
    
  For air 
    
   
  Solving this equation we get, 
   m = 76.5 g 
  This is also percentage of N
2
 by mass on air as total mass we have taken is 100 g. 
6.  n
1
= n
2
 
   
    
7.   Number of gram moles 
  Avogadro number N
A
 = 6.02 × 10
23
/g-mol  
  ?  Total number of molecules, 
   N =nN
A
= 3.34 × 10
22
 
  ?  Number of molecules per cm
2
 
    
8.  (a) Molar heat capacity and heat capacity 
   C
p 
= nC
P
 
  Similarly   C
V
 = nC
V
 
  Now   C
p 
- C
V 
= n (C
P
 - C
V
) - nR 
   
  (b) 
   = (3.5) (2.5) (8.31)= 72.75 J/K  
  C
V
 = nC
V
 = n = (3.5) (1.5) (8.31)= 43.65 J/K 
(c)   
   = (3.5) (3.5) (8.31) = 101.8 J/K 
    = (3.5) (2.5) (8.31)= 72.75 J/K 
9.  (a) As discussed in the above problem.  
   C
V
 = nC
V
 
   
  (b) Internal energy 
Page 5


Introductory Exercise 17.2 
Q 1.  From the graph for an ideal gas state whether m
1
 or m
2
 is greater? 
 
Q 2.  A vessel is filled with an ideal gas at a pressure of 20 atm and is at a temperature of 27°C. One-
half of the mass is removed from the vessel and the temperature of the remaining gas is increased 
to 87°C. At this temperature find the pressure of the gas. 
Q 3.  A vessel contains a mixture of 7 g of nitrogen and 11 g of carbondioxide at temperature T = 290K. 
If pressure of the mixture is 1 atm (=1.01 × 10
5
 N/m
2
), calculate its density (R = 8.31 J/mol-K). 
Q 4.  An electric bulb of volume 250 cm
3
 was sealed off during manufacture at a pressure of 10
-3
 mm of 
mercury at 27°C. Compute the number of air molecules contained in the bulb. Given that R = 8.31 
J/mol -K and N
A
 = 6.02 × 10
23
 per mol. 
Q 5.  State whether P
1
 > P
2
 or P
2
 > P
1
 for given mass of a gas? 
 
Q 6.  For a given mass of a gas what is the shape of P versus 
1
V
graph at constant temperature?  
Solutions 
1.  
   
  At constant volume T -P graph is a straight line of slope, 
  Slope of m
1
 is less. Hence m
1
 is greater. 
2.  
   
3.   n
1
 = number of moles of nitrogen n
2
 = number of moles of CO
2
 = 
   
   
4.  PV = nRT 
   
    
   = 1.33 × 10
-8
 
  ?  Number of molecular = (n)  
   N
A 
= (1.33 × 10
-8
) (6.02 × 10
23
) = 8 × 10
15
 
 5.    
  For given mass, V-T graph is a straight line passing through origin having 
    
  Slope of P
2
 is more. Hence P
2
< P
1
. 
6.  
  i.e., P versus 
1
V
graph is a straight line passing through origin of slope nRT. 
 
Introductory Exercise 17.3 
Q 1.  The average speed of all the molecules in a gas at a given instant is not zero, whereas the average 
velocity of all the molecules is zero. Explain why? 
Q 2.  A sample of helium gas is at a temperature of 300 K and a pressure of 0.5 atm. What is the 
average kinetic energy of a molecule of a gas? 
Q 3.  A sample of helium and neon gases has a temperature of 300 K and pressure of 1.0 atm. The molar 
mass of helium is 4.0 g/mol and that of neon is 20.2 g/mol. 
  (a) Find the rms speed of the helium atoms and of the neon atoms. 
  (b) What is the average kinetic energy per atom of each gas?  
Q 4.  At what temperature will the particles in a sample of helium gas have an rms speed of 1.0 km/s? 
Q 5.  At 0°C and 1.0 atm (=1.01 × 10
5
 N/m
2
) pressure the densities of air, oxygen and nitrogen are 
1.284 kg/m
3
, 1.429 kg/m
3
 and 1.251 kg/m
3
 respectively. Calculate the percentage of nitrogen in 
the air from these data, assuming only these two gases to be present. 
Q 6.  An air bubble of 20 cm
3
 volume is at the bottom of a lake 40 meters deep where the temperature is 
4°C. The bubble rises to the surface which is at a temperature of 20°C. Take the temperature to be 
the same as that of the surrounding water and find its volume just before it reaches the surface. 
Q 7.  If the water molecules in 1.0 g of water were distributed uniformly over the surface of earth, how 
many such molecules would there be in 1.0 cm
2
 of earth's surface? 
Q 8.  For a certain gas the heat capacity at constant pressure is greater than that at constant volume by 
29.1J/K. 
  (a) How many moles of the gas are there? 
  (b) If the gas is monoatomic, what are heat capacities at constant volume and pressure ? 
(c) If the gas molecules are diatomic which rotate but do not vibrate, what are heat capacities at 
constant volume and at constant pressure. 
Q 9.  The heat capacity at constant volume of a sample of a monoatomic gas is 35 J/K. Find : 
  (a) the number of moles  (b) the internal energy at 0°C 
  (c) the molor heat capacity at constant pressure. 
Q 10.  For any distribution of speeds v
rms
 ? v
av
.
 
Is this statement true or false? 
Solutions 
1.  See the answer 
2.  Helium gas is monoatomic. So its degree of freedom f = 3. Average kinetic energy of 1 molecule 
of gas 
    
    
   = 6.21 × 10
-21 
J 
3.  (a) 
  For He gas : 
   = 1368 m/s 
  For Ne gas : 
   = 609 m/s 
  (b) Each gas is monotonic for which degree of freedom f = 3. Hence average kinetic energy of one 
atom 
    
   = 6.21 × 10
-21
 J 
4.   
   
5.  Let mass of nitrogen = (m) g. Then mass of oxygen = (100 - m) g. Number of moles of nitrogen, 
    and number of moles of oxygen 
    
  For air 
    
   
  Solving this equation we get, 
   m = 76.5 g 
  This is also percentage of N
2
 by mass on air as total mass we have taken is 100 g. 
6.  n
1
= n
2
 
   
    
7.   Number of gram moles 
  Avogadro number N
A
 = 6.02 × 10
23
/g-mol  
  ?  Total number of molecules, 
   N =nN
A
= 3.34 × 10
22
 
  ?  Number of molecules per cm
2
 
    
8.  (a) Molar heat capacity and heat capacity 
   C
p 
= nC
P
 
  Similarly   C
V
 = nC
V
 
  Now   C
p 
- C
V 
= n (C
P
 - C
V
) - nR 
   
  (b) 
   = (3.5) (2.5) (8.31)= 72.75 J/K  
  C
V
 = nC
V
 = n = (3.5) (1.5) (8.31)= 43.65 J/K 
(c)   
   = (3.5) (3.5) (8.31) = 101.8 J/K 
    = (3.5) (2.5) (8.31)= 72.75 J/K 
9.  (a) As discussed in the above problem.  
   C
V
 = nC
V
 
   
  (b) Internal energy 
    
  f = degree of freedom = 3 
   
  (c) 
10.  Suppose n
1
 molecules have v
1
 velocity and n
2 
molecules have v
2
 velocity. Then 
      
  Now, v
rms
 ? V
av
 
because v
1
 and v
2
 may be in opposite direction also. 
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