The internal energy change in a system that has absorbed 2 kcal of heat and done 500 J of work is

Heat given to a system ($∆$Q) is equal to the sum of increase in the internal energy ($∆$u) and the work done ( $∆$W) by the system against the surrounding and I cal  = 4.22 J.

According to first law of thermodynamics.

$∆\mathrm{U} = \mathrm{Q} - \mathrm{W}$

 = $2 \times 4.2 \times 1000-500 = 7900 \mathrm{J}$