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?

Short answer

(a) The first law of thermodynamics states that energy cannot be created or destroyed, but can only be transferred or converted from one form to another. This can be represented as: \( \Delta E_{total} = Q + W \), where \( \Delta E_{total} \) is the total change in energy, Q is the heat absorbed/released, and W is the work done by/on the system. (b) The internal energy of a system refers to the combined energy of all the particles within that system. This energy includes the kinetic energy from particle motion and potential energy due to forces such as electromagnetic forces acting between particles. (c) The internal energy of a closed system can increase primarily by two means: 1) heat transfer (e.g. heating water) and 2) work done on the system (e.g. compressing a gas). Any increase in internal energy must be balanced by a decrease in internal energy elsewhere, or an increase in another form of energy according to the first law of thermodynamics.

Step-by-step solution

(a) First Law of Thermodynamics

The first law of thermodynamics states that energy cannot be created or destroyed, but can only be transferred or converted from one form to another. Mathematically, it can be represented as: $$ \Delta E_{total} = Q + W $$ where \( \Delta E_{total} \) is the total change in energy of the system, Q is the heat absorbed or released by the system, and W is the work done by or on the system.

(b) Internal Energy of a System

The internal energy of a system refers to the combined energy of all the particles (atoms or molecules) within that system. This energy includes the kinetic energy of particles resulting from their motion, and the potential energy due to forces acting between the particles such as electromagnetic forces. It can also be defined as the total microscopic energy contained within the system.

(c) Increasing Internal Energy of a Closed System

The internal energy of a closed system can increase primarily by two means: 1. Heat transfer: The internal energy increases when heat is added to the system. For example, when heating water, the kinetic energy of water molecules increases as they absorb the heat, raising the internal energy of the water. 2. Work done on the system: The internal energy increases when work is done on the system. For example, compressing a gas by applying external pressure will increase the internal energy of the gas, as the potential energy between the particles and their kinetic energy increase due to the compression. It is important to note that, in a closed system, any increase in internal energy must be balanced by a decrease in the internal energy of another system, or an increase in another form of energy (like potential or kinetic energy of the system), in accordance with the first law of thermodynamics.