Problem 23 - Chemistry: The Central Science

Question

(a) State the first law of thermodynamics. (b) What is meant by the internal energy of a system? (c) By what means can the internal energy of a closed system increase?

Step-by-Step Solution

Answer

(a) The first law of thermodynamics states that energy cannot be created or destroyed in an isolated system, and the change in internal energy (\(\Delta U\)) is equal to the difference between the heat added to the system (\(Q\)) and the work done by the system on the surroundings (\(W\)), represented by the formula: \[ \Delta U = Q - W \] (b) The internal energy of a system is the total energy stored within a system, including the sum of kinetic and potential energies of its particles. It is a state variable, depending only on the system's current state. (c) The internal energy of a closed system can be increased by adding heat to the system (\(Q > 0\)) or by doing work on the system (\(W < 0\)). The internal energy will increase when the combination of these two factors (\(Q - W\)) results in a positive value according to the first law of thermodynamics.

Step 1: (a) Stating the First Law of Thermodynamics

The first law of thermodynamics, also known as the law of energy conservation, states that energy cannot be created or destroyed in an isolated system. The change in the internal energy of a system is equal to the difference between the heat added to the system and the work done by the system on the surroundings, which can be represented by the formula: \[ \Delta U = Q - W \] Where \(\Delta U\) denotes the change in internal energy, \(Q\) represents the heat added to the system, and \(W\) is the work done by the system on its surroundings.

Step 2: (b) Meaning of Internal Energy of a System

The internal energy of a system refers to the total energy stored within a system. It is the sum of all the kinetic and potential energies of the particles (atoms, molecules, or particles) that constitute the system. Internal energy is a state variable, which means that its value depends on the current state of the system and not on the process or path the system went through to reach that state.

Step 3: (c) Increasing the Internal Energy of a Closed System

The internal energy of a closed system can be increased in two ways: 1. By adding heat to the system (\(Q > 0\)): When heat is transferred to a system, its internal energy increases as the energy is absorbed by the particles in the system, which increases their kinetic and/or potential energy. 2. By doing work on the system (\(W < 0\)): When work is done on a system, energy is transferred into the system. This increases the internal energy of the system as particles gain energy, thus increasing their kinetic and/or potential energy. It is important to note that the internal energy will increase when the combination of these two factors (\(Q - W\)) results in a positive value according to the first law of thermodynamics.