c_P and c_V are specific heats at constant pr | vedclass

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(C) The relation between molar specific heat capacities $C_P$ and $C_V$ is given by Mayer's relation: $C_P - C_V = R$,where $R$ is the universal gas c

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$a = 14b$

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(C) The relation between molar specific heat capacities $C_P$ and $C_V$ is given by Mayer's relation: $C_P - C_V = R$,where $R$ is the universal gas constant.The specific heat capacity $c$ (per unit mass) is related to the molar specific heat capacity $C$ by the relation $c = \frac{C}{M}$,where $M$ is the molar mass of the gas.Therefore,$c_P - c_V = \frac{C_P - C_V}{M} = \frac{R}{M}$.For hydrogen gas $(H_2)$,the molar mass $M_H = 2 \ g/mol$. Thus,$a = \frac{R}{2}$.For nitrogen gas $(N_2)$,the molar mass $M_N = 28 \ g/mol$. Thus,$b = \frac{R}{28}$.Taking the ratio: $\frac{a}{b} = \frac{R/2}{R/28} = \frac{28}{2} = 14$.Therefore,$a = 14b$.

$c_P$ and $c_V$ are specific heats at constant pressure and constant volume respectively. It is observed that
$c_P - c_V = a$ for hydrogen gas
$c_P - c_V = b$ for nitrogen gas
The correct relation between $a$ and $b$ is

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$c_P$ and $c_V$ are specific heats at constant pressure and constant volume respectively. It is observed that$c_P - c_V = a$ for hydrogen gas$c_P - c_V = b$ for nitrogen gasThe correct relation between $a$ and $b$ is