A system releases 622 kJ of heat and does 105 kJ of work on the surroundings. What is the change in internal energy of the system?

Understanding the concept of internal energy is crucial when studying thermodynamics. Internal energy is the total energy contained within a system, encompassing both the kinetic energy of particles moving and vibrating, and the potential energy of particles interacting with each other. A change in internal energy, represented as \( \Delta U \), can occur through varying the system's temperature or phase, or through chemical reactions.

When approaching problems involving internal energy, remember that this value is related to the system's state, and not the path it takes to reach that state. Thus, if a system releases heat or performs work, it's expected to lose internal energy. This principle is precisely illustrated in the exercise where the system releases heat and does work, leading to a negative change in internal energy (\( \Delta U = -727 \text{kJ} \)), indicating that the system's overall energy has decreased.

Heat exchange is a fundamental concept in thermodynamics that must be appreciated when dissecting energy transformations. It represents the transfer of thermal energy between a system and its surroundings. By convention, when a system absorbs heat, the value for heat exchange (\( q \)) is positive, while a negative \( q \) signifies heat release.

In our example, the system releases 622 kJ of heat, which implies a negative heat exchange value (\( q = -622 \text{ kJ} \)). This underlines the principle that the direction of heat flow affects the sign of \( q \), playing a pivotal role in calculating changes to internal energy.

In thermodynamics, work is a form of energy transfer that causes displacement against an opposing force. When discussing the work done by a system, we refer to the work a system performs on its surroundings, like expanding against atmospheric pressure. Work can be done on or by the system, and this affects the internal energy accordingly.

The 'work done by a system', symbolized by \( w \), can be positive or negative. It is positive when the system does work on the surroundings, as seen in our exercise (\( w = 105 \text{kJ} \)). This reflects that energy is used by the system to perform work, thus leading to a decrease in the system’s internal energy. Remember, unlike heat, work is a path function which means it depends on how the system transitions from one state to another.