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Gas Laws - Assignment, Physics Class 12 Notes | EduRev

Class 12 : Gas Laws - Assignment, Physics Class 12 Notes | EduRev

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Course PHYSICS260
Assignment 5
Consider ten grams of nitrogen gas at an initial pressure of 6.0 atm and at room
temperature.
It undergoes an isobaric expansion resulting in a quadrupling of its volume.
(i) After this expansion, what is the gas volume?
(ii) Determine the gas temperature after this step.
In the next process, the gas pressure is decreased at constant volume until the original
temperature is reached.
(iii) After this decrease in gas pressure, what is the value of the pressure?
In the final process, the gas is retured to its initial volume by isothermally compressing it.
(iv) Determine the final gas pressure.
(v) Using appropriate scales on both axes, show the full three-step process on a p - V
diagram.

Introduction to the Ideal Gas Law
Description: Practice using the ideal gas law with a series of questions in which all
but two gas parameters are held fixed.
Learning Goal: To understand the ideal gas law and be able to apply it to a wide
variety of situations.
Page 2

Course PHYSICS260
Assignment 5
Consider ten grams of nitrogen gas at an initial pressure of 6.0 atm and at room
temperature.
It undergoes an isobaric expansion resulting in a quadrupling of its volume.
(i) After this expansion, what is the gas volume?
(ii) Determine the gas temperature after this step.
In the next process, the gas pressure is decreased at constant volume until the original
temperature is reached.
(iii) After this decrease in gas pressure, what is the value of the pressure?
In the final process, the gas is retured to its initial volume by isothermally compressing it.
(iv) Determine the final gas pressure.
(v) Using appropriate scales on both axes, show the full three-step process on a p - V
diagram.

Introduction to the Ideal Gas Law
Description: Practice using the ideal gas law with a series of questions in which all
but two gas parameters are held fixed.
Learning Goal: To understand the ideal gas law and be able to apply it to a wide
variety of situations.
The absolute temperature , volume , and pressure of a gas sample are related by
the ideal gas law, which states that
.
Here is the number of moles in the gas sample and is a gas constant that applies to
all gases. This empirical law describes gases well only if they are sufficiently dilute
and at a sufficiently high temperature that they are not on the verge of condensing.
In applying the ideal gas law, must be the absolute pressure, measured with respect to
vacuum and not with respect to atmospheric pressure, and must be the absolute
temperature, measured in kelvins (that is, with respect to absolute zero). If is in
pascals and is in cubic meters, use . If is in atmospheres and
Part A
A gas sample enclosed in a rigid metal container at room temperature (20 ) has an
absolute pressure . The container is immersed in hot water until it warms to 40 .
What is the new absolute pressure ?
Part A.1 How to approach the problem
To find the final pressure, you must first determine which quantities in the ideal gas
law remain constant in the given situation. Note that is always a constant.
Determine which of the other four quantities are constant for the process described
in this part.
Check all that apply.

Now manipulate the ideal gas law ( ) so that , , and , the constants in
this situation, are isolated on the right side of the equation:
.
Since the right side of the equation is a constant in this situation, the quantity ,
which is always equal to , must be the same at the beginning and the end of
Page 3

Course PHYSICS260
Assignment 5
Consider ten grams of nitrogen gas at an initial pressure of 6.0 atm and at room
temperature.
It undergoes an isobaric expansion resulting in a quadrupling of its volume.
(i) After this expansion, what is the gas volume?
(ii) Determine the gas temperature after this step.
In the next process, the gas pressure is decreased at constant volume until the original
temperature is reached.
(iii) After this decrease in gas pressure, what is the value of the pressure?
In the final process, the gas is retured to its initial volume by isothermally compressing it.
(iv) Determine the final gas pressure.
(v) Using appropriate scales on both axes, show the full three-step process on a p - V
diagram.

Introduction to the Ideal Gas Law
Description: Practice using the ideal gas law with a series of questions in which all
but two gas parameters are held fixed.
Learning Goal: To understand the ideal gas law and be able to apply it to a wide
variety of situations.
The absolute temperature , volume , and pressure of a gas sample are related by
the ideal gas law, which states that
.
Here is the number of moles in the gas sample and is a gas constant that applies to
all gases. This empirical law describes gases well only if they are sufficiently dilute
and at a sufficiently high temperature that they are not on the verge of condensing.
In applying the ideal gas law, must be the absolute pressure, measured with respect to
vacuum and not with respect to atmospheric pressure, and must be the absolute
temperature, measured in kelvins (that is, with respect to absolute zero). If is in
pascals and is in cubic meters, use . If is in atmospheres and
Part A
A gas sample enclosed in a rigid metal container at room temperature (20 ) has an
absolute pressure . The container is immersed in hot water until it warms to 40 .
What is the new absolute pressure ?
Part A.1 How to approach the problem
To find the final pressure, you must first determine which quantities in the ideal gas
law remain constant in the given situation. Note that is always a constant.
Determine which of the other four quantities are constant for the process described
in this part.
Check all that apply.

Now manipulate the ideal gas law ( ) so that , , and , the constants in
this situation, are isolated on the right side of the equation:
.
Since the right side of the equation is a constant in this situation, the quantity ,
which is always equal to , must be the same at the beginning and the end of
the process. Therefore, set . Plug in the values given in this part and
then solve for , the final pressure.
Part A.2 Convert temperatures to kelvins
To apply the ideal gas law, all temperatures must be in absolute units (i.e., in
kelvins). What is the initial temperature in kelvins?
=
0
20
100
273
293

The Celsius and Kelvin temperature scales have the same unit size, so to convert
from degrees Celsius to kelvins, just add 273.
=

This modest temperature increase (in absolute terms) leads to a pressure increase of
just a few percent. Note that it is critical for the temperatures to be converted to
absolute units. If you had used Celsius temperatures, you would have predicted that
the pressure should double, which is far greater than the actual increase.
Part B
Nitrogen gas is introduced into a large deflated plastic bag. No gas is allowed to
escape, but as more and more nitrogen is added, the bag inflates to accommodate it.
The pressure of the gas within the bag remains at 1 and its temperature remains at
room temperature (20 ). How many moles have been introduced into the bag by
the time its volume reaches 22.4 ?
Hint B.1 How to approach the problem
Rearrange the ideal gas law to isolate . Be sure to use the value for in units that
are consistent with the rest of the problem and hence will cancel out to leave moles
at the end.
=

One mole of gas occupies 22.4 at STP (standard temperature and pressure: 0 and
1 ). This fact may be worth memorizing. In this problem, the temperature is
slightly higher than STP, so the gas expands and 22.4 can be filled by slightly less
than 1 of gas.
Page 4

Course PHYSICS260
Assignment 5
Consider ten grams of nitrogen gas at an initial pressure of 6.0 atm and at room
temperature.
It undergoes an isobaric expansion resulting in a quadrupling of its volume.
(i) After this expansion, what is the gas volume?
(ii) Determine the gas temperature after this step.
In the next process, the gas pressure is decreased at constant volume until the original
temperature is reached.
(iii) After this decrease in gas pressure, what is the value of the pressure?
In the final process, the gas is retured to its initial volume by isothermally compressing it.
(iv) Determine the final gas pressure.
(v) Using appropriate scales on both axes, show the full three-step process on a p - V
diagram.

Introduction to the Ideal Gas Law
Description: Practice using the ideal gas law with a series of questions in which all
but two gas parameters are held fixed.
Learning Goal: To understand the ideal gas law and be able to apply it to a wide
variety of situations.
The absolute temperature , volume , and pressure of a gas sample are related by
the ideal gas law, which states that
.
Here is the number of moles in the gas sample and is a gas constant that applies to
all gases. This empirical law describes gases well only if they are sufficiently dilute
and at a sufficiently high temperature that they are not on the verge of condensing.
In applying the ideal gas law, must be the absolute pressure, measured with respect to
vacuum and not with respect to atmospheric pressure, and must be the absolute
temperature, measured in kelvins (that is, with respect to absolute zero). If is in
pascals and is in cubic meters, use . If is in atmospheres and
Part A
A gas sample enclosed in a rigid metal container at room temperature (20 ) has an
absolute pressure . The container is immersed in hot water until it warms to 40 .
What is the new absolute pressure ?
Part A.1 How to approach the problem
To find the final pressure, you must first determine which quantities in the ideal gas
law remain constant in the given situation. Note that is always a constant.
Determine which of the other four quantities are constant for the process described
in this part.
Check all that apply.

Now manipulate the ideal gas law ( ) so that , , and , the constants in
this situation, are isolated on the right side of the equation:
.
Since the right side of the equation is a constant in this situation, the quantity ,
which is always equal to , must be the same at the beginning and the end of
the process. Therefore, set . Plug in the values given in this part and
then solve for , the final pressure.
Part A.2 Convert temperatures to kelvins
To apply the ideal gas law, all temperatures must be in absolute units (i.e., in
kelvins). What is the initial temperature in kelvins?
=
0
20
100
273
293

The Celsius and Kelvin temperature scales have the same unit size, so to convert
from degrees Celsius to kelvins, just add 273.
=

This modest temperature increase (in absolute terms) leads to a pressure increase of
just a few percent. Note that it is critical for the temperatures to be converted to
absolute units. If you had used Celsius temperatures, you would have predicted that
the pressure should double, which is far greater than the actual increase.
Part B
Nitrogen gas is introduced into a large deflated plastic bag. No gas is allowed to
escape, but as more and more nitrogen is added, the bag inflates to accommodate it.
The pressure of the gas within the bag remains at 1 and its temperature remains at
room temperature (20 ). How many moles have been introduced into the bag by
the time its volume reaches 22.4 ?
Hint B.1 How to approach the problem
Rearrange the ideal gas law to isolate . Be sure to use the value for in units that
are consistent with the rest of the problem and hence will cancel out to leave moles
at the end.
=

One mole of gas occupies 22.4 at STP (standard temperature and pressure: 0 and
1 ). This fact may be worth memorizing. In this problem, the temperature is
slightly higher than STP, so the gas expands and 22.4 can be filled by slightly less
than 1 of gas.
Part C
Some hydrogen gas is enclosed within a chamber being held at 200 with a volume
of 0.025 . The chamber is fitted with a movable piston. Initially, the pressure in the
gas is (about 1.5 ). The piston is slowly extracted until the pressure
in the gas falls to . What is the final volume of the container? Assume
that no gas escapes and that the temperature remains at 200 .
Part C.1 How to approach the problem
To find the final volume, you must first determine which quantities in the ideal gas
law remain constant in the given situation. Note that is always a constant.
Determine which of the other four quantities are constant for the process described
in this part.
Check all that apply.

Now look at the ideal gas law: . Since , , and are all constants in this
situation, the quantity , which is always equal to , must be the same at the
beginning and the end of the process. Therefore, set . Plug in the values
given in this part and then solve for , the final volume.

=

Notice how is not needed to answer this problem and neither is , although you do
make use of the fact that is a constant.
Part D
Some hydrogen gas is enclosed within a chamber being held at 200 whose volume
is 0.025 . Initially, the pressure in the gas is (about 15 ). The
chamber is removed from the heat source and allowed to cool until the pressure in the
gas falls to . At what temperature does this occur?
Part D.1 How to approach the problem
To find the final temperature, you must first determine which quantities in the ideal
gas law remain constant in the given situation. Note that is always a constant.
Page 5

Course PHYSICS260
Assignment 5
Consider ten grams of nitrogen gas at an initial pressure of 6.0 atm and at room
temperature.
It undergoes an isobaric expansion resulting in a quadrupling of its volume.
(i) After this expansion, what is the gas volume?
(ii) Determine the gas temperature after this step.
In the next process, the gas pressure is decreased at constant volume until the original
temperature is reached.
(iii) After this decrease in gas pressure, what is the value of the pressure?
In the final process, the gas is retured to its initial volume by isothermally compressing it.
(iv) Determine the final gas pressure.
(v) Using appropriate scales on both axes, show the full three-step process on a p - V
diagram.

Introduction to the Ideal Gas Law
Description: Practice using the ideal gas law with a series of questions in which all
but two gas parameters are held fixed.
Learning Goal: To understand the ideal gas law and be able to apply it to a wide
variety of situations.
The absolute temperature , volume , and pressure of a gas sample are related by
the ideal gas law, which states that
.
Here is the number of moles in the gas sample and is a gas constant that applies to
all gases. This empirical law describes gases well only if they are sufficiently dilute
and at a sufficiently high temperature that they are not on the verge of condensing.
In applying the ideal gas law, must be the absolute pressure, measured with respect to
vacuum and not with respect to atmospheric pressure, and must be the absolute
temperature, measured in kelvins (that is, with respect to absolute zero). If is in
pascals and is in cubic meters, use . If is in atmospheres and
Part A
A gas sample enclosed in a rigid metal container at room temperature (20 ) has an
absolute pressure . The container is immersed in hot water until it warms to 40 .
What is the new absolute pressure ?
Part A.1 How to approach the problem
To find the final pressure, you must first determine which quantities in the ideal gas
law remain constant in the given situation. Note that is always a constant.
Determine which of the other four quantities are constant for the process described
in this part.
Check all that apply.

Now manipulate the ideal gas law ( ) so that , , and , the constants in
this situation, are isolated on the right side of the equation:
.
Since the right side of the equation is a constant in this situation, the quantity ,
which is always equal to , must be the same at the beginning and the end of
the process. Therefore, set . Plug in the values given in this part and
then solve for , the final pressure.
Part A.2 Convert temperatures to kelvins
To apply the ideal gas law, all temperatures must be in absolute units (i.e., in
kelvins). What is the initial temperature in kelvins?
=
0
20
100
273
293

The Celsius and Kelvin temperature scales have the same unit size, so to convert
from degrees Celsius to kelvins, just add 273.
=

This modest temperature increase (in absolute terms) leads to a pressure increase of
just a few percent. Note that it is critical for the temperatures to be converted to
absolute units. If you had used Celsius temperatures, you would have predicted that
the pressure should double, which is far greater than the actual increase.
Part B
Nitrogen gas is introduced into a large deflated plastic bag. No gas is allowed to
escape, but as more and more nitrogen is added, the bag inflates to accommodate it.
The pressure of the gas within the bag remains at 1 and its temperature remains at
room temperature (20 ). How many moles have been introduced into the bag by
the time its volume reaches 22.4 ?
Hint B.1 How to approach the problem
Rearrange the ideal gas law to isolate . Be sure to use the value for in units that
are consistent with the rest of the problem and hence will cancel out to leave moles
at the end.
=

One mole of gas occupies 22.4 at STP (standard temperature and pressure: 0 and
1 ). This fact may be worth memorizing. In this problem, the temperature is
slightly higher than STP, so the gas expands and 22.4 can be filled by slightly less
than 1 of gas.
Part C
Some hydrogen gas is enclosed within a chamber being held at 200 with a volume
of 0.025 . The chamber is fitted with a movable piston. Initially, the pressure in the
gas is (about 1.5 ). The piston is slowly extracted until the pressure
in the gas falls to . What is the final volume of the container? Assume
that no gas escapes and that the temperature remains at 200 .
Part C.1 How to approach the problem
To find the final volume, you must first determine which quantities in the ideal gas
law remain constant in the given situation. Note that is always a constant.
Determine which of the other four quantities are constant for the process described
in this part.
Check all that apply.

Now look at the ideal gas law: . Since , , and are all constants in this
situation, the quantity , which is always equal to , must be the same at the
beginning and the end of the process. Therefore, set . Plug in the values
given in this part and then solve for , the final volume.

=

Notice how is not needed to answer this problem and neither is , although you do
make use of the fact that is a constant.
Part D
Some hydrogen gas is enclosed within a chamber being held at 200 whose volume
is 0.025 . Initially, the pressure in the gas is (about 15 ). The
chamber is removed from the heat source and allowed to cool until the pressure in the
gas falls to . At what temperature does this occur?
Part D.1 How to approach the problem
To find the final temperature, you must first determine which quantities in the ideal
gas law remain constant in the given situation. Note that is always a constant.
Determine which of the other four quantities are constant for the process described
in this part.
Check all that apply.

Now manipulate the ideal gas law ( ) so that , , and , the constants in
this situation, are isolated on the right side of the equation:
.
Since the right side of the equation is a constant in this part, the quantity ,
which is always equal to , must be the same at the beginning and the end of
the process. Therefore, set . Plug in the values given in this part and
then solve for , the final temperature.

=

This final temperature happens to be close to room temperature. Hydrogen remains a
gas to temperatures well below that, but if this question had been about water vapor,
for example, the gas would have condensed to liquid water at 100 and the ideal gas
law would no longer have applied.

Understanding pV Diagrams
Description: Several qualitative and conceptual questions related to pV-diagrams.
Learning Goal: To understand the meaning and the basic applications of pV diagrams
for an ideal gas.
As you know, the parameters of an ideal gas are described by the equation
,
where is the pressure of the gas, is the volume of the gas, is the number of moles,
is the universal gas constant, and is the absolute temperature of the gas. It follows
that, for a portion of an ideal gas,
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