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NEETChemistryThermodynamics (C)

For an ideal gas, the molar heat capacity at constant pressure is C_p and at constant volume is C_v . If the heat capacity ratio is = C_p C_v and R is the universal gas constant, which of the following expressions correctly represents C_p ?

Options

  1. AR - 1
  2. BR - 1
  3. CR
  4. DR

Correct answer

B. R - 1

Step-by-step solution

For one mole of an ideal gas, Mayer's relation states that: C_p - C_v = R We are given that = C_p C_v , which implies C_v = C_p . Substituting this into Mayer's relation: C_p - C_p = R Factoring out C_p gives: C_p (1 - 1 ) = R C_p ( - 1 ) = R Rearranging to solve for C_p yields: C_p = R - 1 Note that R - 1 is the expression for C_v . Answer: R - 1

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