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An ideal gas occupies an unknown volume V liters (L) at a pressure of 12 atm. The gas is
expanded isothermally against a constant external pressure of 2 atm so that its final volume
becomes 3 L. The work involved for this expansion process is ....cal. (Round off to
two decimal places)
?
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An ideal gas occupies an unknown volume V liters (L) at a pressure of ...
Solution:
Given data:
Initial pressure, P1 = 12 atm
Initial volume, V1 = ?
Final volume, V2 = 3 L
External pressure, Pext = 2 atm
Isothermal process:
For an isothermal process, the temperature remains constant. Therefore, the ideal gas equation is given as:
PV = nRT
Where,
P = pressure
V = volume
n = number of moles
R = universal gas constant
T = temperature
Since the temperature remains constant, we can write:
P1V1 = P2V2
Where,
P1 = initial pressure
V1 = initial volume
P2 = final pressure
V2 = final volume
Solving the above equation for V1, we get:
V1 = P2V2/P1
V1 = (2 atm)(3 L)/(12 atm)
V1 = 0.5 L
Work done:
The work done for an isothermal expansion is given by:
W = -nRT ln(V2/V1)
Where,
n = number of moles
R = universal gas constant
T = temperature
V1 = initial volume
V2 = final volume
Since the temperature remains constant, we can write:
W = -nRT ln(V2/V1)
W = -(Pext)(V2 - V1) ln(V2/V1)
W = -(2 atm)(3 L - 0.5 L) ln(3 L/0.5 L)
W = -10.77 cal
Therefore, the work involved for this expansion process is -10.77 cal (negative sign indicates work done by the system).
Given data:
Initial pressure, P1 = 12 atm
Initial volume, V1 = ?
Final volume, V2 = 3 L
External pressure, Pext = 2 atm
Isothermal process:
For an isothermal process, the temperature remains constant. Therefore, the ideal gas equation is given as:
PV = nRT
Where,
P = pressure
V = volume
n = number of moles
R = universal gas constant
T = temperature
Since the temperature remains constant, we can write:
P1V1 = P2V2
Where,
P1 = initial pressure
V1 = initial volume
P2 = final pressure
V2 = final volume
Solving the above equation for V1, we get:
V1 = P2V2/P1
V1 = (2 atm)(3 L)/(12 atm)
V1 = 0.5 L
Work done:
The work done for an isothermal expansion is given by:
W = -nRT ln(V2/V1)
Where,
n = number of moles
R = universal gas constant
T = temperature
V1 = initial volume
V2 = final volume
Since the temperature remains constant, we can write:
W = -nRT ln(V2/V1)
W = -(Pext)(V2 - V1) ln(V2/V1)
W = -(2 atm)(3 L - 0.5 L) ln(3 L/0.5 L)
W = -10.77 cal
Therefore, the work involved for this expansion process is -10.77 cal (negative sign indicates work done by the system).
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An ideal gas occupies an unknown volume V liters (L) at a pressure of 12 atm. The gas is
expanded isothermally against a constant external pressure of 2 atm so that its final volume
becomes 3 L. The work involved for this expansion process is ....cal. (Round off to
two decimal places) Related: General Organic Chemistry - General Organic Chemistry, Organic Chemistry?
Question Description
An ideal gas occupies an unknown volume V liters (L) at a pressure of 12 atm. The gas is expanded isothermally against a constant external pressure of 2 atm so that its final volume becomes 3 L. The work involved for this expansion process is ....cal. (Round off to two decimal places) Related: General Organic Chemistry - General Organic Chemistry, Organic Chemistry? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about An ideal gas occupies an unknown volume V liters (L) at a pressure of 12 atm. The gas is expanded isothermally against a constant external pressure of 2 atm so that its final volume becomes 3 L. The work involved for this expansion process is ....cal. (Round off to two decimal places) Related: General Organic Chemistry - General Organic Chemistry, Organic Chemistry? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An ideal gas occupies an unknown volume V liters (L) at a pressure of 12 atm. The gas is expanded isothermally against a constant external pressure of 2 atm so that its final volume becomes 3 L. The work involved for this expansion process is ....cal. (Round off to two decimal places) Related: General Organic Chemistry - General Organic Chemistry, Organic Chemistry?.
An ideal gas occupies an unknown volume V liters (L) at a pressure of 12 atm. The gas is expanded isothermally against a constant external pressure of 2 atm so that its final volume becomes 3 L. The work involved for this expansion process is ....cal. (Round off to two decimal places) Related: General Organic Chemistry - General Organic Chemistry, Organic Chemistry? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about An ideal gas occupies an unknown volume V liters (L) at a pressure of 12 atm. The gas is expanded isothermally against a constant external pressure of 2 atm so that its final volume becomes 3 L. The work involved for this expansion process is ....cal. (Round off to two decimal places) Related: General Organic Chemistry - General Organic Chemistry, Organic Chemistry? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An ideal gas occupies an unknown volume V liters (L) at a pressure of 12 atm. The gas is expanded isothermally against a constant external pressure of 2 atm so that its final volume becomes 3 L. The work involved for this expansion process is ....cal. (Round off to two decimal places) Related: General Organic Chemistry - General Organic Chemistry, Organic Chemistry?.
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expanded isothermally against a constant external pressure of 2 atm so that its final volume
becomes 3 L. The work involved for this expansion process is ....cal. (Round off to
two decimal places) Related: General Organic Chemistry - General Organic Chemistry, Organic Chemistry? in English & in Hindi are available as part of our courses for IIT JAM.
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expanded isothermally against a constant external pressure of 2 atm so that its final volume
becomes 3 L. The work involved for this expansion process is ....cal. (Round off to
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An ideal gas occupies an unknown volume V liters (L) at a pressure of 12 atm. The gas is
expanded isothermally against a constant external pressure of 2 atm so that its final volume
becomes 3 L. The work involved for this expansion process is ....cal. (Round off to
two decimal places) Related: General Organic Chemistry - General Organic Chemistry, Organic Chemistry?, a detailed solution for An ideal gas occupies an unknown volume V liters (L) at a pressure of 12 atm. The gas is
expanded isothermally against a constant external pressure of 2 atm so that its final volume
becomes 3 L. The work involved for this expansion process is ....cal. (Round off to
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expanded isothermally against a constant external pressure of 2 atm so that its final volume
becomes 3 L. The work involved for this expansion process is ....cal. (Round off to
two decimal places) Related: General Organic Chemistry - General Organic Chemistry, Organic Chemistry? theory, EduRev gives you an
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expanded isothermally against a constant external pressure of 2 atm so that its final volume
becomes 3 L. The work involved for this expansion process is ....cal. (Round off to
two decimal places) Related: General Organic Chemistry - General Organic Chemistry, Organic Chemistry? tests, examples and also practice IIT JAM tests.
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