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NEETChemistryThermodynamics (C)

During the reversible isothermal compression of one mole of an ideal gas at 300 K , the work done on the gas is 5744 J . What is the ratio of its final volume to its initial volume ( V_f V_i ) ? (Given: 2.303 R 300 = 5744 J )

Options

  1. A10
  2. B0.1
  3. C-1
  4. D1

Correct answer

B. 0.1

Step-by-step solution

For a reversible isothermal process, the work done is given by: W = -2.303 nRT ( V_f V_i ) Since work is done on the gas (compression), W is positive according to IUPAC sign conventions. W = +5744 J Substituting the given values ( n = 1 mole ): 5744 = -1 (2.303 R 300) ( V_f V_i ) We are given that 2.303 R 300 = 5744 J . 5744 = -5744 ( V_f V_i ) ( V_f V_i ) = -1 Taking the antilog on both sides: V_f V_i = 10⁻¹ = 0.1 The ratio of the final volume to the initial volume is 0.1 . Answer: 0.1

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