For an ideal gas,the value of ${\left( {\frac{{dU}}{{dV}}} \right)_T}$ is ...... .

The density of gas $A$ is twice that of gas $B$ at the same temperature. The molecular weight of gas $B$ is twice that of gas $A$. The ratio of the pressure of gas $A$ to gas $B$ will be:

$A$ certain sample of gas has a volume of $0.2 \ L$ measured at $1 \ atm$ pressure and $0 \ ^oC$. At the same pressure but at $273 \ ^oC$,its volume will be ................ $L$.

When the applied pressure is $16 \ atm$,the temperature is $27 \ ^oC$,and the volume is $9 \ L$,what will be the weight of $CH_4$ gas in $gm$? (Given $R = 0.08 \ L \ atm \ K^{-1} \ mol^{-1}$)

Calculate the new pressure of a gas enclosed in a cylinder when it is compressed from $5 \text{ L}$ to $2 \text{ L}$ at an initial pressure of $1 \text{ atm}$ and temperature of $300 \text{ K}$. The final temperature in this process is $500 \text{ K}$. (in $\text{ atm}$)

The density of acetic acid vapor at $300 \ K$ and $1 \ atm$ is $5 \ mg \ cm^{-3}$. The number of acetic acid molecules in the cluster that is formed in the gas phase is closest to