Question

For a monoatomic gas, the molar specific heat at constant pressure divided by the molar gas constant $R$ is equal to

• A. $2.5$
• B. $1.5$
• C. $5.0$
• D. $3.5$
• E. $4.0$

Answer 1

The correct option is A $2.5$

For a monoatomic gas,
$\frac{C_P}{C_V}=\gamma =1.67$
or $C_P-1.67C_V=0...\left(i\right)$
$C_P-C_V=R....\left(ii\right)$
On multiplying Eq. (ii) by $1.67$ and subtracting Eq. (i) from it, we get
$0.67C_P=167R$
$\frac{C_P}{R}=\frac{167}{0.67}$
$\frac{C_P}{R}=2.492=2.5$.