The change in internal energy of a thermodynamic system which has absorbed 2 kcal of heat and done
400 J of work is (Take, 1 cal = 4.2 J)

According to first law of thermodynamics,

$Q=\mathrm{\Delta }U+W$

$Q=2\mathrm{kcal}=2000\times 4.2=8400\mathrm{J}$

$W=400\mathrm{J}$

$\Rightarrow 8400=\mathrm{\Delta }U+400$

$\mathrm{\Delta }U=8400-400$

$\mathrm{\Delta }U=8000\mathrm{J}$

Change in internal energy,  $\mathrm{\Delta }U=8\mathrm{kJ}$