$A$ diatomic ideal gas is used in a Carnot engine as the working substance. If during the adiabatic expansion part of the cycle the volume of the gas increases from $V$ to $32V$,the efficiency of the engine is

The molar heat of formation of $NH_4NO_{3(s)}$ is $-367.54 \ kJ$ and those of $N_2O_{(g)}$ and $H_2O_{(l)}$ are $+81.46 \ kJ$ and $-285.78 \ kJ$ respectively at $25 \ ^oC$ and $1.0 \ atm$ pressure. Calculate $\Delta U$ at $25 \ ^oC$ for the reaction:
$NH_4NO_{3(s)} \to N_2O_{(g)} + 2H_2O_{(l)}$ (in $kJ$)

If a solid sphere of mass $1 \ kg$ and radius $0.1 \ m$ rolls without slipping at a uniform velocity of $1 \ m/s$ along a straight line on a horizontal floor,the kinetic energy is

The number of molecules of $CO_2$ liberated by the complete combustion of $0.1 \text{ mol}$ of graphite in air is:

Consider the following statements about Langmuir isotherm.
$I.$ The free gas and adsorbed gas are in dynamic equilibrium.
$II.$ All adsorption sites are equivalent.
$III.$ The initially adsorbed layer can act as a substrate for further adsorption.
$IV.$ The ability of a molecule to get adsorbed at a given site is independent of the occupation of neighboring sites.
The correct statements are

Which of the following would produce a buffer solution when mixed in equal volumes?