In the context of thermodynamics, entropy is a measure of the disorder or randomness of a system. During an irreversible process, the entropy of a system generally increases. To calculate the entropy change mathematically, you can use the concept of entropy production.
Entropy production is a measure of the rate at which entropy is generated within a system due to irreversible processes. It is denoted by the symbol "σ" and has units of entropy per unit time. The total change in entropy of a system during an irreversible process can be obtained by integrating the entropy production over the duration of the process.
Mathematically, the change in entropy (ΔS) of a system undergoing an irreversible process can be expressed as:
ΔS = ∫ σ dt
Here, the integral represents the integration of entropy production (σ) with respect to time (t) over the duration of the process. The entropy production rate, σ, depends on the specific irreversible processes occurring within the system, such as heat transfer, friction, or chemical reactions.
It's important to note that calculating the exact value of entropy production can be complex and often requires detailed knowledge of the system and the underlying processes. In practical scenarios, simplified models or assumptions are often made to estimate or approximate the entropy change during irreversible processes.