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The change in entropy of 2 moles of an ideal gas upon iosthermal expansion at 243.6 K from 20 litre until the pressure becomes 1 atm, is :
- a)1.385 cal/K
- b)–1.2 cal/k
- c)1.2 cal/K
- d)2.77 cal/K
Correct answer is option 'D'. Can you explain this answer?
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To find the change in entropy of an ideal gas during an isothermal expansion, we can use the formula:
ΔS = nR ln(V2/V1)
Where:
ΔS is the change in entropy
n is the number of moles of the gas
R is the gas constant
V1 is the initial volume of the gas
V2 is the final volume of the gas
Given:
n = 2 moles
R = 8.314 J/mol·K (gas constant)
T = 243.6 K (temperature)
V1 = 20 L (initial volume)
P2 = 1 atm (final pressure)
Converting the initial volume to m^3:
V1 = 20 L = 0.02 m^3
Using the ideal gas law to find the final volume:
P1V1 = P2V2
(1 atm)(0.02 m^3) = (1 atm)(V2)
V2 = 0.02 m^3
Substituting the given values into the entropy change formula:
ΔS = (2 mol)(8.314 J/mol·K) ln(0.02 m^3 / 0.02 m^3)
ΔS = 16.628 J/K
Since the given options are in cal/K, we need to convert J to cal:
1 cal = 4.184 J
Converting the entropy change to cal/K:
ΔS = 16.628 J/K * (1 cal / 4.184 J)
ΔS ≈ 3.975 cal/K
Therefore, the correct answer is option D) 2.77 cal/K.
ΔS = nR ln(V2/V1)
Where:
ΔS is the change in entropy
n is the number of moles of the gas
R is the gas constant
V1 is the initial volume of the gas
V2 is the final volume of the gas
Given:
n = 2 moles
R = 8.314 J/mol·K (gas constant)
T = 243.6 K (temperature)
V1 = 20 L (initial volume)
P2 = 1 atm (final pressure)
Converting the initial volume to m^3:
V1 = 20 L = 0.02 m^3
Using the ideal gas law to find the final volume:
P1V1 = P2V2
(1 atm)(0.02 m^3) = (1 atm)(V2)
V2 = 0.02 m^3
Substituting the given values into the entropy change formula:
ΔS = (2 mol)(8.314 J/mol·K) ln(0.02 m^3 / 0.02 m^3)
ΔS = 16.628 J/K
Since the given options are in cal/K, we need to convert J to cal:
1 cal = 4.184 J
Converting the entropy change to cal/K:
ΔS = 16.628 J/K * (1 cal / 4.184 J)
ΔS ≈ 3.975 cal/K
Therefore, the correct answer is option D) 2.77 cal/K.
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The change in entropy of 2 moles of an ideal gas upon iosthermal expansion at 243.6 K from 20 litre until the pressure becomes 1 atm, is :a)1.385 cal/Kb)–1.2 cal/kc)1.2 cal/Kd)2.77 cal/KCorrect answer is option 'D'. Can you explain this answer?
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The change in entropy of 2 moles of an ideal gas upon iosthermal expansion at 243.6 K from 20 litre until the pressure becomes 1 atm, is :a)1.385 cal/Kb)–1.2 cal/kc)1.2 cal/Kd)2.77 cal/KCorrect answer is option 'D'. Can you explain this answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about The change in entropy of 2 moles of an ideal gas upon iosthermal expansion at 243.6 K from 20 litre until the pressure becomes 1 atm, is :a)1.385 cal/Kb)–1.2 cal/kc)1.2 cal/Kd)2.77 cal/KCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The change in entropy of 2 moles of an ideal gas upon iosthermal expansion at 243.6 K from 20 litre until the pressure becomes 1 atm, is :a)1.385 cal/Kb)–1.2 cal/kc)1.2 cal/Kd)2.77 cal/KCorrect answer is option 'D'. Can you explain this answer?.
The change in entropy of 2 moles of an ideal gas upon iosthermal expansion at 243.6 K from 20 litre until the pressure becomes 1 atm, is :a)1.385 cal/Kb)–1.2 cal/kc)1.2 cal/Kd)2.77 cal/KCorrect answer is option 'D'. Can you explain this answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about The change in entropy of 2 moles of an ideal gas upon iosthermal expansion at 243.6 K from 20 litre until the pressure becomes 1 atm, is :a)1.385 cal/Kb)–1.2 cal/kc)1.2 cal/Kd)2.77 cal/KCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The change in entropy of 2 moles of an ideal gas upon iosthermal expansion at 243.6 K from 20 litre until the pressure becomes 1 atm, is :a)1.385 cal/Kb)–1.2 cal/kc)1.2 cal/Kd)2.77 cal/KCorrect answer is option 'D'. Can you explain this answer?.
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