Which one of the following is the correct relation between Cp and Cv for one mole of an ideal gas? (R is molar gas constant)
- Cp=Cv-R
- Cp=Cv+R
- Cp=R-Cv
- Cp=Cv×R
- \(C_P=\frac{C_V}{R}\)
The Correct Option is B
Approach Solution - 1
For an ideal gas, the relation between the heat capacities at constant pressure (\(C_P\)) and constant volume (\(C_V\)) is given by: \[ C_P - C_V = R \] where \( R \) is the universal gas constant. Therefore, the correct relation between \( C_P \) and \( C_V \) is: \[ C_P = C_V + R \]
The correct option is (B) : \(C_p=C_v+R\)
Approach Solution -2
For one mole of an ideal gas, the correct relation between the molar specific heats at constant pressure (Cp) and constant volume (Cv) is given by the equation: Cp = Cv + R Where R is the universal gas constant. This is derived from the first law of thermodynamics and the definitions of specific heat capacities.
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