(a) According to the first law of thermodynamics, what quantity is conserved? (b) What is meant by the internal energy of a system? (c) By what means can the internal energy of a closed system increase?

The first law of thermodynamics states that the energy in a closed system is conserved, meaning that the total energy cannot be created nor destroyed. Mathematically, the first law of thermodynamics can be expressed as: \[ΔE_\text{internal} = Q - W,\] where \( ΔE_\text{internal} \) is the change in the system's internal energy, \( Q \) is the heat added to or removed from the system, and \( W \) represents the work done on or by the system.

The internal energy of a system is the total of all kinetic and potential energies associated with the microscopic particles (like atoms or molecules) of the system. These microscopic particles are in constant motion and interact with each other, resulting in the kinetic and potential energies present within the system. The internal energy is a measure of the system's energy required to maintain these microscopic motions and interactions. It may change due to heat transfer, work being done on or by the system, or internal processes (like chemical reactions).

The internal energy of a closed system can be increased mainly through two means: 1. Adding heat (Q): When heat is added to the closed system, the energy transfer increases the microscopic motions and the interactions among the particles in the system, thus increasing the internal energy. According to the first law of thermodynamics, this increase can be represented by a positive value for Q in the equation \( ΔE_\text{internal} = Q - W \). 2. Doing work on the system (W): When work is done on (or received by) the system, it increases the system's energy. For instance, if we compress a gas in a closed container, we are doing work on the system, and this energy transfer can subsequently cause an increase in the internal energy. To represent a positive increase in internal energy due to work done on the system, W should be negative in the equation \( ΔE_\text{internal} = Q - W \), as it is defined as the work done by the system.