According to the first law of thermodynamics,which of the following is correct? (Where $q =$ heat supplied to the system and $W =$ work done by the system)

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

Which of the following is the correct expression of the first law of thermodynamics for adiabatic processes?

For combustion of one mole of magnesium in an open container at $300 \ K$ and $1 \ bar$ pressure,$\Delta_{C}H^{\ominus} = -601.70 \ kJ \ mol^{-1}$,the magnitude of change in internal energy for the reaction is $.... \ kJ$. (Nearest integer)
(Given : $R = 8.3 \ J \ K^{-1} \ mol^{-1}$ )

In an adiabatic process,no transfer of heat takes place between the system and surroundings. Choose the correct option for the free expansion of an ideal gas under adiabatic conditions from the following:

Calculate the quantity of heat released from a system when $2 \text{ moles}$ of an ideal gas are compressed isothermally from a volume of $25 \text{ dm}^3$ to $10 \text{ dm}^3$ at a constant external pressure of $4 \text{ bar}$. (in $\text{ kJ}$)