The gas in a piston (defined as the system) warms and absorbs 655 J of heat. The expansion performs 344 J of work on thesurroundings. What is the change in internal energy for the system?

Internal energy is a key concept in thermodynamics, representing the total energy within a system due to the random motion and position of its particles. It includes various forms of kinetic and potential energy that are associated with the movement and interactions of these particles. In the context of gases in a piston, the internal energy is influenced by temperature, volume, and the number of particles.

When a gas in a piston heats up and expands, as in our original exercise, this typically leads to an increase in the internal energy of the system because the particles are moving more vigorously and have greater kinetic energy. It's important to note that internal energy is a state function; it depends only on the current state of the system, not on how that state was reached. This is why we can use heat absorption and work done by the system to determine the change in internal energy.

Heat absorption refers to the transfer of energy into a system in the form of heat. In thermodynamics, this is often discussed as a process that can change the internal energy of a system. Heat can be transferred in various ways, including conduction, convection, and radiation, but in all cases, it results in an increase in the system's internal energy, assuming no other changes such as work done occur concurrently.

Our example problem states that the gas within the piston absorbs 655 J of heat. This heat transfer will mostly contribute to the increase of the kinetic energy of the gas particles, leading to a higher temperature and internal energy of the gas. One of the key points to understand here is that heat is a form of energy transfer rather than a form of energy contained within an object or system.

In thermodynamics, work done by a system usually involves a force causing a displacement. If the system is a gas within a piston, as we see in our exercise, work is done when the gas expands against an external pressure, moving the piston. This is energy leaving the system in the form of work, and in accordance with the first law of thermodynamics, it leads to a decrease in the internal energy of the system.

In the situation described, the gas performs 344 J of work on its surroundings. This does not mean that the energy disappears; rather, it's transferred to the surroundings as the system does work on the external environment. Essentially, the internal energy that was added to the system from heat absorption is partially used to do this work. The first law of thermodynamics shows us how the balance of these two processes results in the change in internal energy.