For a gas,$R/C_V = 0.67$. What kind of molecules is this gas made of?

What is the relationship between the internal energy $U$ of an ideal gas and its pressure $P$ and volume $V$?

When $40 \ J$ of heat is absorbed by a monatomic gas,the increase in the internal energy of the gas is (in $J$)

Match the List-$I$ with List-$II$:

List-$I$	List-$II$
$A$. Triatomic rigid gas	$I$. $\frac{C_P}{C_V} = \frac{5}{3}$
$B$. Diatomic non-rigid gas	$II$. $\frac{C_P}{C_V} = \frac{7}{5}$
$C$. Monoatomic gas	$III$. $\frac{C_P}{C_V} = \frac{4}{3}$
$D$. Diatomic rigid gas	$IV$. $\frac{C_P}{C_V} = \frac{9}{7}$

Choose the correct answer from the options given below:

The heat energy required to raise the temperature of $5 \, moles$ of an ideal gas by $5 \, K$ at constant pressure is $600 \, J$. How much heat (in $J$) is required to raise the same mass of the same gas by $5 \, K$ at constant volume? (Take $R = 8.3 \, J/mol \cdot K$)

The ratio of molar specific heats of oxygen is