Which of the following is the correct option for the free expansion of an ideal gas under adiabatic conditions?

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

$1 \, \text{mole}$ of an ideal gas is allowed to expand reversibly and adiabatically from a temperature of $27^{\circ}C$. The work done is $3 \, \text{kJ} \, \text{mol}^{-1}$. The final temperature of the gas is $...... \text{K}$ (Nearest integer). Given $C_{V} = 20 \, \text{J} \, \text{mol}^{-1} \, \text{K}^{-1}$.

Calculate the change in internal energy of the system if $20 \ kJ$ of work is done on the system and it releases $10 \ kJ$ of heat in a particular reaction. (in $kJ$)

$A$ system receives $100 \ cal$ of heat,and at the same time,$50 \ cal$ of work is done by the system. Calculate the change in internal energy. (in $cal$)

$A$ system does $394 \ J$ of work on the surroundings by absorbing $701 \ J$ of heat. What is the change in internal energy of the system (in $J$)?