Question

If separate samples of argon, methane, nitrogen and carbon dioxide, all at the same initial temperature and pressure and expanded adiabatically reversibally to double their origin 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

Given

$N_2$, $C{H}_4$, $C{O}_2$, Ar are kept at same temp and pressure

Volume is doubled

Solution

For adiabatically reversible expansion we use Poisson equation

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

As $V_2=2\ast V_1$

$T_2=2^{(1-r)}\ast T_1$

Less is the r More is the $T_2$

$r=\frac{C_p}{C_v}$

More is the $C_v$ less is the r and more is the $T_2$

$C_v$ depends on the no. of atoms in a molecule

As methane have highest no. of atoms that is 5\Therefore it will have highest $C_v$ and Highest final temperature.

The correct option is C