Question

If separate samples of argon, methane, nitrogen and carbon dioxide, all at the same initial temperature and pressure and expanded adiabatically reversiblly to double their original volumes, then which one of these gases will have high temperature as final temperature?

• A. Nitrogen
• B. Argon
• C. Methane
• D. Carbon dioxide

Answer 1

The correct option is C Methane

For adiabatic reversible expansion we use Poisson Equation

$T_1{V}_1^{r-1}=T_2{V}_2^{r-1}$

or,

$\frac{T_1}{T_2}={\left(\frac{V_2}{V_1}\right)}^{r-1}$

As the volume is getting doubled,

Thus, $T_1=(2{)}^{r+},T_2$

or, $T_2=T_1(2{)}^{(1-r)}$

Thus, less the va;ue of $r$, more will be the value of $T_2$

$r=\frac{C_P}{C_V}$

Thus, more the $C_V$, the less will be the $1e-r$.

$C_V$ depends upon number of atom in any molecule. More the number of atoms, more will be the $C_V$. Thus $C{H}_4$, methane has $5$ atoms thus will have higher value of $C_V$ as degree of freedom is $3\times 5=15$. Therefore it will have lowest value of $r$ and hence will have highest final temperature $T_2$.