When a system absorbs $8 \ kJ$ of heat and does $2.2 \ kJ$ of work on the surroundings,calculate the internal energy change. (in $kJ$)

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

$A$ 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 $.....\, kJ$.

The heat change for the following reaction at $298 \ K$ and at constant pressure is $+7.3 \ kcal$: $A_2B_{(s)} \to 2A_{(s)} + 1/2B_{2(g)}$,$\Delta H = +7.3 \ kcal$. The heat change at constant volume would be:

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

$A$ 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 $cal$)