DC Pandey Solutions: Thermometry, Thermal Expansion & Kinetic Theory of Gases - 2

# DC Pandey Solutions: Thermometry, Thermal Expansion & Kinetic Theory of Gases - 2 | Physics Class 11 - NEET PDF Download

``` 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
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
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
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
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
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.
```

## Physics Class 11

102 videos|411 docs|121 tests

## FAQs on DC Pandey Solutions: Thermometry, Thermal Expansion & Kinetic Theory of Gases - 2 - Physics Class 11 - NEET

 1. What is thermometry?
Ans. Thermometry is the measurement of temperature using various instruments and techniques. It involves the use of thermometers to quantify the degree of hotness or coldness of an object or substance. Thermometry plays a crucial role in various fields, including scientific research, industrial processes, and everyday life.
 2. How does thermal expansion occur?
Ans. Thermal expansion occurs when an object or material expands or contracts in response to changes in temperature. As the temperature increases, the molecules within the object gain kinetic energy and move more vigorously, causing them to spread apart. This results in an increase in the overall size or volume of the object. Conversely, when the temperature decreases, the molecules lose energy and move closer together, leading to a decrease in size or volume.
 3. What is the kinetic theory of gases?
Ans. The kinetic theory of gases is a model that explains the behavior and properties of gases based on the motion of their particles. According to this theory, gases consist of a large number of tiny particles (atoms or molecules) that are in constant random motion. The theory explains various gas properties, such as pressure, temperature, volume, and the relationship between them.
 4. How does a mercury thermometer work?
Ans. A mercury thermometer works based on the principle of thermal expansion of liquids. Inside the glass tube of the thermometer, there is a small bulb filled with mercury. As the temperature increases, the mercury expands, causing it to rise up the narrow capillary tube. The temperature is determined by reading the height of the mercury column against a calibrated scale on the thermometer.
 5. What are some common methods of temperature measurement?
Ans. Some common methods of temperature measurement include using mercury or alcohol-filled thermometers, infrared thermometers, thermocouples, resistance temperature detectors (RTDs), and thermistors. Each method has its own advantages and applications, depending on the temperature range, accuracy requirements, and environmental conditions.

## Physics Class 11

102 videos|411 docs|121 tests

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