Which one of the following is applicable for an adiabatic expansion of an ideal gas?

$A$ mixture of gas expands from $0.03\, m^3$ to $0.06\, m^3$ at a constant pressure of $1\, MPa$ and absorbs $84\, kJ$ of heat during the process. The change in internal energy of the mixture is $.....\, kJ$.

$A$ gas can be taken from state $A$ to state $B$ via two different paths $ACB$ and $ADB$. When path $ACB$ is used, $60 \text{ J}$ of heat flows into the system and $30 \text{ J}$ of work is done by the system. If path $ADB$ is used, the work done by the system is $10 \text{ J}$. The heat flow into the system in path $ADB$ is: (in $text{ J}$)

In the complete combustion of butanol $C_4H_9OH_{(l)}$,if $\Delta H$ is the enthalpy of combustion and $\Delta E$ is the heat of combustion at constant volume,then

For a reaction,$A_{(g)} \to A_{(l)}$; $\Delta H = -3RT$. The correct statement for the reaction is

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