What is the difference between $\Delta H$ and $\Delta U$ for the reaction given below at $298 \ K$ (in $kJ$)? $(R = 8.314 \ J \ K^{-1} \ mol^{-1})$
$2 \ C_6H_{6(\ell)} + 15 \ O_{2(g)} \rightarrow 12 \ CO_{2(g)} + 6 \ H_2O_{(\ell)}$

$5 \, mol$ of an ideal gas expands isothermally and irreversibly from a pressure of $10 \, atm$ to $1 \, atm$ against a constant external pressure of $1 \, atm$. The work done $(w_{irr})$ at $300 \, K$ is:

When $1 \ mole$ of gas is heated at constant volume,the temperature rises from $273 \ K$ to $546 \ K$. If heat supplied to the gas is $x \ J$,then find the correct statement from the following.

Calculate the internal energy change of one mole of an ideal gas during an adiabatic free expansion process from a volume of $2 \ L$ to $5 \ L$.

For water $\Delta_{vap} H = 41 \ kJ \ mol^{-1}$ at $373 \ K$ and $1 \ bar$ pressure. Assuming that water vapour is an ideal gas that occupies a much larger volume than liquid water,the internal energy change during evaporation of water is $...... \ kJ \ mol^{-1}$.
[Use: $R = 8.3 \ J \ mol^{-1} \ K^{-1}$]

Which of the following relations is correct for the internal energy change $(\Delta U)$ in a process occurring at constant volume?