(a) Calculate the work for a system that absorbs \(150 \mathrm{~kJ}\) of heat in a process for which the increase in internal energy is \(120 \mathrm{~kJ}\). (b) Is work done on or by the system during this process?

Thermodynamics is a branch of physics that deals with the relationships between heat and other forms of energy. It is a fundamental subject that applies to a wide range of fields from mechanical engineering to chemistry. The key principle it explores is how heat is converted to and from other energy forms and how it affects matter. It encompasses various laws, with the first law, also known as the law of energy conservation, serving as the cornerstone for understanding energy transfers within a system.

When studying thermodynamics, it's essential to recognize the system and surroundings. The system is the part of the universe we are focusing on, while the surroundings include everything else. Energy can be exchanged between these two through heat and work, which are the ways systems interact with their surroundings. Understanding thermodynamics helps us to grapple with how energy is conserved and transformed, which is paramount in many scientific and engineering challenges.

Internal energy is a concept from thermodynamics referring to the total energy contained within a system. It encompasses all forms of energy including kinetic energy from the movement of the atoms and molecules, potential energy from the bonds between those atoms, and more. The significance of internal energy is that it is a property of the system that changes only when energy crosses the system boundary by heat transfer or work.

In the context of the first law of thermodynamics, the change in internal energy \( \Delta U \) is equal to the energy added to the system through heat \( Q \) minus the energy that leaves the system in the form of work \( W \). This relationship is encapsulated in the formula \( \Delta U = Q - W \). In a physical sense, when a system absorbs heat, its internal energy increases, which might result in an increase in temperature or a change in the system's state, such as melting ice turning into water.

In thermodynamics, 'work done' refers to the amount of energy transferred by the system through force applied over a distance. It is a crucial concept that describes how systems interact with their environment. For example, compressing a piston in a cylinder or spinning a turbine entails work done by or on the system. The first law of thermodynamics relates work done to changes in internal energy and heat transfer.

Work is often represented as \( W \) in equations and is measured in joules in the International System of Units (SI). The sign of work done can indicate the direction of energy transfer: positive work is done when the system expands against external pressure, and negative work is done when the environment does work on the system (as in compression). In the case of the given exercise, since the work is calculated to be positive, it shows that energy is being dispensed by the system to its surroundings.

Heat transfer is the movement of thermal energy from one thing to another because of a temperature difference. It plays a pivotal role in thermodynamics and can occur in three primary ways: conduction, convection, and radiation. In conduction, heat is transferred through direct contact; in convection, it is transferred through the movement of fluids; and in radiation, it travels in electromagnetic waves.

In terms of the first law of thermodynamics, heat transfer is the mechanism that allows systems to exchange energy with their surroundings. When a system absorbs heat, indicated by a positive \( Q \), its internal energy typically increases unless the system also does work on the surroundings or undergoes a phase change. Understanding heat transfer is instrumental for all sorts of applications, including designing heating and cooling systems, industrial processes, and even for understanding natural phenomena like weather patterns.