Work Done In Isothermal Expansion
Two moles of an ideal gas expand isothermally at 300 K from a volume V to a volume 2V in a slow reversible manner, so what is the work done by the gas? Take R = 8.3 J per mol kelvin.
Select the correct option:
Solution
3453 J
As derived in NCERT Class 11, Chapter 12 (Thermodynamics), the work done by an ideal gas in a reversible isothermal expansion is W=nRTln(ViVf), where n is the number of moles and the temperature is constant. Here n=2, T=300 K, and ViVf=V2V=2, so ln2≈0.693. Substituting: W=2×8.3×300×0.693=4980×0.693≈3453 J. Since temperature is constant, Δcup=0 and all this work is supplied by heat absorbed from the surroundings. The option 4980 J is wrong because it omits the ln2 factor, using nRT alone. The option 1726 J is wrong because it uses one mole instead of two. The option 6906 J is wrong because it doubles the correct value, perhaps using ln4 or a factor error. A plausibility check on magnitude confirms the answer: nRT=2×8.3×300=4980 J, and multiplying by ln2<1 must give a value below 4980 J, which the result of 3453 J indeed satisfies, so the magnitude and the logarithmic dependence are both reasonable.
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About This Question
- Subject
- physics
- Chapter
- thermodynamics
- Topic
- work done in isothermal expansion
- Difficulty
- Hard
- Year
- 2025
Solution
Correct Answer:
3453 J
As derived in NCERT Class 11, Chapter 12 (Thermodynamics), the work done by an ideal gas in a reversible isothermal expansion is W=nRTln(ViVf), where n is the number of moles and the temperature is constant. Here n=2, T=300 K, and ViVf=V2V=2, so ln2≈0.693. Substituting: W=2×8.3×300×0.693=4980×0.693≈3453 J. Since temperature is constant, Δcup=0 and all this work is supplied by heat absorbed from the surroundings. The option 4980 J is wrong because it omits the ln2 factor, using nRT alone. The option 1726 J is wrong because it uses one mole instead of two. The option 6906 J is wrong because it doubles the correct value, perhaps using ln4 or a factor error. A plausibility check on magnitude confirms the answer: nRT=2×8.3×300=4980 J, and multiplying by ln2<1 must give a value below 4980 J, which the result of 3453 J indeed satisfies, so the magnitude and the logarithmic dependence are both reasonable.
This hard difficulty physics question is from the chapter thermodynamics, covering the topic of work done in isothermal expansion. It appeared in the 2025 exam.
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