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NEETChemistryThermodynamics (C)

If C_P and C_V represent the total heat capacities at constant pressure and constant volume respectively for n moles of an ideal gas, which of the following relationships is correct?

Options

  1. AC_P - C_V = R
  2. BC_P - C_V = R n
  3. CC_P - C_V = nR
  4. DC_P - C_V = 0

Correct answer

C. C_P - C_V = nR

Step-by-step solution

For 1 mole of an ideal gas, the molar heat capacities are related by Mayer's relation: C_ p,m - C_ v,m = R . For n moles of the gas, the total (extensive) heat capacity at constant pressure is C_P = nC_ p,m and at constant volume is C_V = nC_ v,m . Substituting these into the relation gives: C_P n - C_V n = R Multiplying the entire equation by n , we get: C_P - C_V = nR Answer: C_P - C_V = nR

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