Problem: Classify the following by the sign of delta U for the system: the following can be classified into these three categories (negative,positive, not enough data)1. The system contracts and the surroundings get cooler.2. The system expands and the surroundings get cooler.3. The system contracts and the surroundings get hotter.4. The system expands and the surroundings get hotter.

We are being asked to classify the sign of delta U for the following systems

1. The system contracts and the surroundings get cooler.
2. The system expands and the surroundings get cooler.
3. The system contracts and the surroundings get hotter.
4. The system expands and the surroundings get hotter.

The internal energy (ΔE or ΔU) of a system can be calculated from the heat and work of the system. The relationship between internal energy, heat, and work is shown in the following equation:

$\boxed{\mathbf{\Delta }\mathbf{ }\mathbf{U}\mathbf{ }\mathbf{=}\mathbf{ }\mathbf{q}\mathbf{ }\mathbf{+}\mathbf{ }\mathbf{w}}$

ΔU = internal energy, J

q = heat, J

w = work, J

Before calculating internal energy, we have to identifyheat (q) and work (w) first.

For heat, q:

▪ + q → if the system gains, takes in, or absorbs heat or energy
 ▪ – q → if the system loses, evolves, gives off, or releases heat or energy