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The molar internal energy of a gas at temperature T is Um (T). The mo lar internal energy at T = 0 is Um (0). The correct expression that relates these two with appropriate contributions is:
- a)Um(T) = Um(0) + 3 RT [linear molecule; translation only]
- b)Um(T) = Um(0) + 5/2 RT [linear molecule; translation and rotation only]
- c)Um(T) = Um(0) + 3/2 RT [Non-linear molecule; translation and rotation only]
- d)Um(T) = Um(0) + RT [Non-linear molecule; translation only]
Correct answer is option 'B'. Can you explain this answer?
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The molar internal energy of a gas at temperature T is Um (T). The mo ...
Explanation:
The molar internal energy of a gas at temperature T is Um (T). The molar internal energy at T = 0 is Um (0). The correct expression that relates these two with appropriate contributions is:
Option B: Um(T) = Um(0) + 5/2 RT [linear molecule; translation and rotation only]
Explanation:
For a linear molecule, the internal energy is contributed by translation and rotation only. Therefore, the molar internal energy of a gas at temperature T for a linear molecule can be expressed as:
Um(T) = Um(0) + NfRT
where N is the number of moles of gas, f is the degree of freedom, and R is the gas constant.
For a linear molecule, the degree of freedom is 5, which includes 3 degrees of freedom for translation and 2 degrees of freedom for rotation. Therefore, the expression for the molar internal energy becomes:
Um(T) = Um(0) + 5/2 RT
This is the correct expression that relates the molar internal energy of a gas at temperature T and T=0 for a linear molecule with appropriate contributions.
Conclusion:
Hence, the correct option is B.
The molar internal energy of a gas at temperature T is Um (T). The molar internal energy at T = 0 is Um (0). The correct expression that relates these two with appropriate contributions is:
Option B: Um(T) = Um(0) + 5/2 RT [linear molecule; translation and rotation only]
Explanation:
For a linear molecule, the internal energy is contributed by translation and rotation only. Therefore, the molar internal energy of a gas at temperature T for a linear molecule can be expressed as:
Um(T) = Um(0) + NfRT
where N is the number of moles of gas, f is the degree of freedom, and R is the gas constant.
For a linear molecule, the degree of freedom is 5, which includes 3 degrees of freedom for translation and 2 degrees of freedom for rotation. Therefore, the expression for the molar internal energy becomes:
Um(T) = Um(0) + 5/2 RT
This is the correct expression that relates the molar internal energy of a gas at temperature T and T=0 for a linear molecule with appropriate contributions.
Conclusion:
Hence, the correct option is B.
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The molar internal energy of a gas at temperature T is Um (T). The mo ...
We know (dU/dT)v=Cv. so, dU=CvdT. Um(T)-Um(0)=CvT. And Cv=5/2 RT. Um(T)-Um(0)=5/2 RT. But I am not confirm about the ans. please tell me it is right or not.
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The molar internal energy of a gas at temperature T is Um (T). The mo lar internal energy at T = 0 is Um (0). The correct expression that relates these two with appropriate contributions is:a)Um(T) = Um(0) + 3 RT [linear molecule; translation only]b)Um(T) = Um(0) + 5/2 RT [linear molecule; translation and rotation only]c)Um(T) = Um(0) + 3/2 RT [Non-linear molecule; translation and rotation only]d)Um(T) = Um(0) + RT [Non-linear molecule; translation only]Correct answer is option 'B'. Can you explain this answer?
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The molar internal energy of a gas at temperature T is Um (T). The mo lar internal energy at T = 0 is Um (0). The correct expression that relates these two with appropriate contributions is:a)Um(T) = Um(0) + 3 RT [linear molecule; translation only]b)Um(T) = Um(0) + 5/2 RT [linear molecule; translation and rotation only]c)Um(T) = Um(0) + 3/2 RT [Non-linear molecule; translation and rotation only]d)Um(T) = Um(0) + RT [Non-linear molecule; translation only]Correct answer is option 'B'. Can you explain this answer? for Chemistry 2024 is part of Chemistry preparation. The Question and answers have been prepared according to the Chemistry exam syllabus. Information about The molar internal energy of a gas at temperature T is Um (T). The mo lar internal energy at T = 0 is Um (0). The correct expression that relates these two with appropriate contributions is:a)Um(T) = Um(0) + 3 RT [linear molecule; translation only]b)Um(T) = Um(0) + 5/2 RT [linear molecule; translation and rotation only]c)Um(T) = Um(0) + 3/2 RT [Non-linear molecule; translation and rotation only]d)Um(T) = Um(0) + RT [Non-linear molecule; translation only]Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Chemistry 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The molar internal energy of a gas at temperature T is Um (T). The mo lar internal energy at T = 0 is Um (0). The correct expression that relates these two with appropriate contributions is:a)Um(T) = Um(0) + 3 RT [linear molecule; translation only]b)Um(T) = Um(0) + 5/2 RT [linear molecule; translation and rotation only]c)Um(T) = Um(0) + 3/2 RT [Non-linear molecule; translation and rotation only]d)Um(T) = Um(0) + RT [Non-linear molecule; translation only]Correct answer is option 'B'. Can you explain this answer?.
The molar internal energy of a gas at temperature T is Um (T). The mo lar internal energy at T = 0 is Um (0). The correct expression that relates these two with appropriate contributions is:a)Um(T) = Um(0) + 3 RT [linear molecule; translation only]b)Um(T) = Um(0) + 5/2 RT [linear molecule; translation and rotation only]c)Um(T) = Um(0) + 3/2 RT [Non-linear molecule; translation and rotation only]d)Um(T) = Um(0) + RT [Non-linear molecule; translation only]Correct answer is option 'B'. Can you explain this answer? for Chemistry 2024 is part of Chemistry preparation. The Question and answers have been prepared according to the Chemistry exam syllabus. Information about The molar internal energy of a gas at temperature T is Um (T). The mo lar internal energy at T = 0 is Um (0). The correct expression that relates these two with appropriate contributions is:a)Um(T) = Um(0) + 3 RT [linear molecule; translation only]b)Um(T) = Um(0) + 5/2 RT [linear molecule; translation and rotation only]c)Um(T) = Um(0) + 3/2 RT [Non-linear molecule; translation and rotation only]d)Um(T) = Um(0) + RT [Non-linear molecule; translation only]Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Chemistry 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The molar internal energy of a gas at temperature T is Um (T). The mo lar internal energy at T = 0 is Um (0). The correct expression that relates these two with appropriate contributions is:a)Um(T) = Um(0) + 3 RT [linear molecule; translation only]b)Um(T) = Um(0) + 5/2 RT [linear molecule; translation and rotation only]c)Um(T) = Um(0) + 3/2 RT [Non-linear molecule; translation and rotation only]d)Um(T) = Um(0) + RT [Non-linear molecule; translation only]Correct answer is option 'B'. Can you explain this answer?.
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