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ChemistryNEET 2024First law, enthalpy and Hess's law

Thermodynamics

The work done during the reversible isothermal expansion of one mole of hydrogen gas at 25∘25^\circC from a pressure of 20 atmosphere to 10 atmosphere is (given R=2.0 cal K−1 mol−1R = 2.0\ \mathrm{cal\,K^{-1}\,mol^{-1}}):

  1. A.–413.14 calories✓
  2. B.413.14 calories
  3. C.100 calories
  4. D.0 calorie

Solution

w=−2.303 nRTlog⁡p1p2=−2.303×1×2×298×log⁡2=−413.14w = -2.303\,nRT\log\frac{p_1}{p_2} = -2.303 \times 1 \times 2 \times 298 \times \log 2 = -413.14 cal. Work done by the gas on expansion is negative in the sign convention used.

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