Question

The value of the ratio $C_p/C_v$ for hydrogen is 1.67 at 30 K but decreases to 1.4 at 300 K as more degrees of freedom become active. During this rise in temperature

• A. $C_p$ remains constant but $C_v$ increases
• B. $C_p$ decreases by $C_v$ increases
• C. both $C_p$ and $C_v$ decreases by the same amount
• D. both $C_p$ and $C_v$ increases by the same amount

Answer 1

The correct option is D both $C_p$ and $C_v$ increases by the same amount

he value of the ratio $\frac{Cp}{Cv}$for hydrogen is 1.67 at 30 K but decreases to 1.4 at 300 K as more degrees of freedom become active. During this rise in temperature both $Cp$ and $Cv$ increases by the same amount

For an ideal gas, $C_p=C_v+R$. If it is a molecular gas, increasing temperature enables vibrational degrees of freedom, so that $C_v$ increases. Hence $\frac{C_p}{C_v}=1+\frac{R}{C_v}$ decreases.