According to the First Law of Thermodynamics, the relationship between heat ($Q$), work ($W$), and the change in internal energy ($\Delta U$) is given by $\Delta Q = \Delta U + \Delta W$ (using the standard physics sign convention where work done by the system is positive).

1. Convert Heat to Joules: Given heat absorbed $Q = 2 \text{ kcal} = 2000 \text{ cal}$. Using the mechanical equivalent of heat ($1 \text{ cal} \approx 4.2 \text{ J}$): $Q = 2000 \times 4.2 \text{ J} = 8400 \text{ J}$.

2. Identify Work Done: Work done by the system $W = 500 \text{ J}$.

3. Calculate Internal Energy Change: Rearranging the First Law equation: $\Delta U = Q - W$. $\Delta U = 8400 \text{ J} - 500 \text{ J} = 7900 \text{ J}$.