A system absorbs \(20 \mathrm{~kJ}\) heat and does \(10 \mathrm{~kJ}\) of work. The internal energy of the system (a) increases by \(10 \mathrm{~kJ}\) (b) decreases by \(10 \mathrm{~kJ}\) (c) increases by \(30 \mathrm{~kJ}\) (d) decreases by \(30 \mathrm{~kJ}\)

Internal energy is a fundamental concept in thermodynamics, representing the total energy contained within a system. It encompasses all forms of energy within the system, which for a typical system include the kinetic energy of particles, potential energy due to intermolecular forces, and other more complex forms of energy. In simpler terms, it's the energy associated with the microscopic components of the system, such as molecules, atoms, and subatomic particles.

When we look at a system in terms of thermodynamics, we don't measure the actual value of internal energy but instead focus on the changes in internal energy, denoted as \(\Delta U\). Changes in internal energy occur through heat exchange with the surroundings or through work done by or on the system, aligning with the principles of the First Law of Thermodynamics.

Heat absorption refers to the transfer of energy into a system from its surroundings due to a temperature difference. This heat transfer is often symbolized as \(Q\) in thermodynamic equations. In our everyday experience, when a substance absorbs heat, it may undergo a temperature increase or a change in state, such as melting or vaporizing. For instance, when ice absorbs heat, it melts and becomes water.

It's important to note that heat is a form of energy in transit, and any heat that enters a system will contribute to the system's internal energy unless it is counteracted by work done by the system. Contrary to temperature, which is a measure of the average kinetic energy of the particles in a substance, heat is an energy transfer that flows from a hotter object to a cooler one until thermal equilibrium is reached.

In thermodynamics, work done by the system, often abbreviated as \(W\), is the energy transferred when the system exerts a force through a distance. In essence, when a system does work on its surroundings, it might cause a volume change against an external pressure or set another object in motion.

A practical example of work done by a system includes gas within a piston-cylinder assembly. As the gas expands, it pushes against the piston, exerting force over distance, thereby doing work on the piston. In the equation \(\Delta U = Q - W\) from the First Law of Thermodynamics, the work done by the system is subtracted because it represents energy the system is giving away to its surroundings. The ability of a system to do work is also a form of energy storage similar to a battery storing electrical potential energy.

The principle of conservation of energy is a broad concept in physics that applies to various forms of energy, including mechanical, thermal, electrical, chemical, nuclear, and others. In the context of thermodynamics, it is encapsulated within the First Law of Thermodynamics. This law is essentially a statement of energy conservation for thermal systems.

According to the conservation of energy, energy cannot be created or destroyed in an isolated system. Instead, it can only be transformed from one form to another. For example, chemical energy stored in a fuel can be transformed into thermal energy through combustion. In our exercise, the heat absorbed by the system and the work done by the system transform into an increase in internal energy, which is a showcase of energy conservation within a thermodynamic system.