If $2 \ kJ$ of heat is released from the system and $6 \ kJ$ of work is done on the system,what is the internal energy change $(\Delta U)$ of the system?

For $1 \, \text{mol}$ of an ideal gas,isothermal expansion occurs from $1 \, \text{L}$ to $10 \, \text{L}$ in a vacuum at $300 \, \text{K}$. What is the value of $\Delta U$ for this process? $(R = 2 \, \text{cal} \, \text{K}^{-1} \, \text{mol}^{-1})$

Observe the following reaction: $ABO_{3(s)} \xrightarrow{1000 \ K} AO_{(s)} + BO_{2(g)}$. $\Delta_{r} H$ for this reaction is $x \ kJ \ mol^{-1}$. What is its $\Delta_{r} U$ (in $kJ \ mol^{-1}$) at the same temperature? $(R = 8.3 \ J \ mol^{-1} \ K^{-1})$

$A$ gas expands isothermally against a constant external pressure of $1 \ bar$ from $10 \ dm^3$ to $20 \ dm^3$ by absorbing $800 \ J$ of heat from the surroundings. Calculate the value of $\Delta U$. (in $J$)

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

What is the work done during the oxidation of $4 \ mol$ of $SO_{2(g)}$ to $SO_{3(g)}$ at $27^{\circ} C$ (in $kJ$)? $(R = 8.314 \ J \ K^{-1} \ mol^{-1})$