$\Delta U$ is equal to

For an ideal gas,the heat of reaction at constant pressure and heat of reaction at constant volume are related by the equation:

The temperature of a system decreases in which of the following processes?

$A$ mixture of $2 \ mol$ of carbon monoxide and $1 \ mol$ of oxygen in a closed vessel is ignited to convert the carbon monoxide to carbon dioxide. If $\Delta H$ is the enthalpy change and $\Delta E$ is the change in internal energy,then:

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: $R = 8.3 \ J \ mol^{-1} \ K^{-1}$]

When $1 \, \text{mol}$ of a gas is heated at constant volume,the temperature increases from $298 \, K$ to $308 \, K$. If the heat supplied to the gas is $500 \, J$,which of the following statements is correct?