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? $(R = 8.3 \ J \ mol^{-1} \ K^{-1})$

Based on the first law of thermodynamics,which one of the following is correct?

In a $1 \, L$ container,$2 \, mol$ of $CO$ and $1 \, mol$ of $O_2$ are taken. They react according to the equation: $2CO(g) + O_2(g) \rightarrow 2CO_2(g)$,$\Delta H = -560 \, kJ$. Given that $1 \, atm \cdot L = 0.1 \, kJ$,and the pressure changes from $70 \, atm$ to $40 \, atm$ at $500 \, K$,calculate the value of $\Delta U$ in $kJ$.

If $100 \ L$ of an ideal gas at a pressure of $2 \ atm$ is compressed isothermally and reversibly to a final volume of '$X$' $L$ and releases $460.6 \ L \ atm$ of heat,the final volume '$X$' (in $L$) is

During compression of a spring,the work done is $10 \ kJ$ and $2 \ kJ$ escaped to the surroundings as heat. The change in internal energy,$\Delta U$ (in $kJ$),is

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 $5 \ L$.