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The work done per mole in an isothermal process is
- a)RT log10 (V2/V1)
- b)RT log10 (V1/V2)
- c)RT loge (V2/V1)
- d)RT loge(V1/V2)
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The work done per mole in an isothermal process isa)RT log10 (V2/V1)b)...
Work done is given by,
δW = nRT loge V2/V1
Form one mole
δW = RT loge V2/V1
δW = nRT loge V2/V1
Form one mole
δW = RT loge V2/V1
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Community Answer
The work done per mole in an isothermal process isa)RT log10 (V2/V1)b)...
Understanding Isothermal Processes
In an isothermal process, the temperature remains constant while a gas expands or contracts. The work done during this process can be derived from the first law of thermodynamics and the ideal gas law.
Work Done in Isothermal Process
- The formula for work done (W) when a gas expands or compresses is given by:
W = ∫ P dV
- For an ideal gas, pressure (P) can be expressed using the ideal gas equation:
P = nRT/V
- Substituting this into the work integral, we have:
W = ∫ (nRT/V) dV
- This integration occurs from the initial volume (V1) to the final volume (V2).
Integrating the Expression
- The work done then simplifies to:
W = nRT ∫ (1/V) dV from V1 to V2
- Performing this integral yields:
W = nRT [log(V2) - log(V1)]
- This can be further simplified using logarithmic properties:
W = nRT log(V2/V1)
Per Mole of Gas
- Since the question asks for the work done per mole, we set n = 1 (per mole):
W = RT log(V2/V1)
- To express this in terms of natural logarithms, we recognize that:
log(a/b) = log(a) - log(b)
Final Answer
- Thus, the correct expression for work done per mole during an isothermal process is:
W = RT loge(V2/V1)
This corresponds to option 'C', confirming that the work done is related to the natural logarithm of the volume ratio during an isothermal expansion or compression.
In an isothermal process, the temperature remains constant while a gas expands or contracts. The work done during this process can be derived from the first law of thermodynamics and the ideal gas law.
Work Done in Isothermal Process
- The formula for work done (W) when a gas expands or compresses is given by:
W = ∫ P dV
- For an ideal gas, pressure (P) can be expressed using the ideal gas equation:
P = nRT/V
- Substituting this into the work integral, we have:
W = ∫ (nRT/V) dV
- This integration occurs from the initial volume (V1) to the final volume (V2).
Integrating the Expression
- The work done then simplifies to:
W = nRT ∫ (1/V) dV from V1 to V2
- Performing this integral yields:
W = nRT [log(V2) - log(V1)]
- This can be further simplified using logarithmic properties:
W = nRT log(V2/V1)
Per Mole of Gas
- Since the question asks for the work done per mole, we set n = 1 (per mole):
W = RT log(V2/V1)
- To express this in terms of natural logarithms, we recognize that:
log(a/b) = log(a) - log(b)
Final Answer
- Thus, the correct expression for work done per mole during an isothermal process is:
W = RT loge(V2/V1)
This corresponds to option 'C', confirming that the work done is related to the natural logarithm of the volume ratio during an isothermal expansion or compression.
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The work done per mole in an isothermal process isa)RT log10 (V2/V1)b)RT log10 (V1/V2)c)RT loge (V2/V1)d)RT loge(V1/V2)Correct answer is option 'C'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The work done per mole in an isothermal process isa)RT log10 (V2/V1)b)RT log10 (V1/V2)c)RT loge (V2/V1)d)RT loge(V1/V2)Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The work done per mole in an isothermal process isa)RT log10 (V2/V1)b)RT log10 (V1/V2)c)RT loge (V2/V1)d)RT loge(V1/V2)Correct answer is option 'C'. Can you explain this answer?.
The work done per mole in an isothermal process isa)RT log10 (V2/V1)b)RT log10 (V1/V2)c)RT loge (V2/V1)d)RT loge(V1/V2)Correct answer is option 'C'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The work done per mole in an isothermal process isa)RT log10 (V2/V1)b)RT log10 (V1/V2)c)RT loge (V2/V1)d)RT loge(V1/V2)Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The work done per mole in an isothermal process isa)RT log10 (V2/V1)b)RT log10 (V1/V2)c)RT loge (V2/V1)d)RT loge(V1/V2)Correct answer is option 'C'. Can you explain this answer?.
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