Final answer:
The change in internal energy of the system is calculated by converting kcal to joules and kj to joules, then applying the first law of thermodynamics using the formula ΔU = Q - W, where ΔU is the change in internal energy, Q is the heat, and W is the work done.
Step-by-step explanation:
To calculate the change in internal energy of the system based on the provided scenario, we use the first law of thermodynamics, which states: ΔU = Q - W, where ΔU is the change in internal energy, Q is the heat added to the system, and W is the work done by the system.
Firstly, we must ensure that our units for heat (Q) and work (W) are the same. Since work is given in kcal (1 kcal = 4184 J) and heat is provided in kj (1 kj = 1000 J), we convert them to joules:
- Work done to the system: 5 x 10² kcal x 4184 J/kcal = 5 x 10² x 4184 x 10² J
- Heat released by the system: 5 x 10² kj x 1000 J/kj = 5 x 10² x 1000 x 10² J
Now we apply the first law of thermodynamics formula:
ΔU = Q - W = (5 x 10² x 1000 x 10²) J - (5 x 10² x 4184 x 10²) J = (5 x 10´ x 10²) J - (5 x 4184 x 10´) J = (5 x 10´ - 5 x 4184) x 10´ J
Upon simplifying, we find the net change in internal energy (ΔU) for the system.