If a system has 2.50 × 102 kcal of work done to it, and releases 5.00 × 102 kJ of heat into its surroundings, what is the change in internal energy of the system?

Answer 1

The change in internal energy of a system is given by the first law of thermodynamics, which states that the change in internal energy (ΔU) is equal to the heat added to the system (Q) minus the work done by the system (W): ΔU = Q - W.

In this problem, the work is done on the system, so the work term is positive. Also, the heat is released by the system into its surroundings, so the heat term is negative.

First, we need to convert the given values into the same unit, since the work is given in kcal and the heat is given in kJ. We know that 1 kcal = 4.184 kJ. Therefore, the work done (in kJ) is:

W = 2.50 × 10^2 kcal × (4.184 kJ/kcal) = 1.046 × 10^3 kJ

Now, we can calculate the change in internal energy:

ΔU = Q - W
ΔU = -5.00 × 10^2 kJ - 1.046 × 10^3 kJ
ΔU = -1.546 × 10^3 kJ

The change in internal energy of the system is -1.546 × 10^3 kJ.