A system does \(40 \mathrm{~J}\) work on surrounding as well as gives out \(20 \mathrm{~J}\) energy. Calculate the change in internal energy.

The concept of change in internal energy is fundamental when studying thermodynamics. Imagine a system, like a gas in a piston, as appearing stationary, yet its molecules are constantly in motion. The sum of kinetic and potential energies of these molecules constitutes the system's internal energy, often symbolized by 'U'.

The internal energy can change, and these changes occur due to interactions with the environment. When energy is transferred to a system, either by heating it or by doing work on it, 'U' increases. Conversely, if the system loses energy by doing work on its surroundings or releasing heat, as stated in our exercise, 'U' decreases. The exercise clearly shows a system losing energy, emphasizing that the internal energy is not static but dynamic, changing in response to physical processes.

Approaching thermodynamics problems usually involves a few critical steps: identifying known and unknown variables, applying relevant laws, and solving the equations.

Thermodynamics problems range from simple to complex, like calculating a change in internal energy, or predicting the behaviour of real-world engines. The key to solving these problems is a strong grasp of the main laws of thermodynamics, such as conservation of energy, often tested through exercises similar to the one provided.

In our example, clear identification of energy transfers—both work and heat—allows the application of the first law to solve for the change in internal energy. This structured approach is invaluable for tackling all kinds of problems in this domain.

In thermodynamics, the concepts of work and heat are two primary ways energy is transferred to and from a system. Heat can be thought of as energy transferred due to temperature difference, and work as the energy transfer when a force moves an object over a distance.

In the context of our exercise, when the system does 40 J of work on the surroundings, it means energy is being expended to cause some physical change outside the system, be it lifting a weight or compressing a spring.

Heat, on the other hand, is depicted as the 20 J given out by the system, likely by cooling down. The negative sign for heat reflects that this energy is lost by the system. The interplay between work and heat is central in thermodynamic processes, and understanding their relationship is key for solving problems and analyzing energy changes within any given system.