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

At the same temperature,gas $A$ is taken in a $0.5 \, dm^3$ flask and gas $B$ is taken in a $1 \, dm^3$ flask. If the density of $A$ is $3.0 \, g \, dm^{-3}$ and that of $B$ is $1.5 \, g \, dm^{-3}$,and the molar mass of $A$ is $1/2$ of $B$,what is the ratio of the pressures exerted by the gases?

The molecular weights of $O_2$ and $SO_2$ are $32$ and $64$ respectively. If $1 \, L$ of $O_2$ at $15 \, ^\circ C$ and $750 \, mm$ pressure contains '$N$' molecules,the number of molecules in $2 \, L$ of $SO_2$ under the same conditions of temperature and pressure will be

An ideal gas with a molar mass of $40 \ g \ mol^{-1}$ has a mass of $120 \ g$. It occupies a volume of $20 \ L$ at a temperature of $400 \ K$. Using $R = 0.0821 \ L \ atm \ K^{-1} \ mol^{-1}$,the pressure of the gas is ........ $atm$.

The value of the universal gas constant $R$ is the same for all gases. What is its physical significance?

The density of oxygen at $STP$ is $1.43 \, g \, L^{-1}$. What will be its density at $27 \, ^\circ C$ temperature and $700 \, torr$ pressure?