Question

A unit mass of a substance undergoes an irreversible process from state 1 to state 2 while gaining heat from the surroundings at temperature \(T\) in the amount of \(q\). If the entropy of the substance is \(s_{1}\) at state \(1,\) and \(s_{2}\) at state \(2,\) the entropy change of the substance \(\Delta s\) during this process is \((a) \Delta ss_{2}-s_{1}\) \((c) \Delta s=s_{2}-s_{1}\) \((d) \Delta s=s_{2}-s_{1}+q / T\) \((e) \Delta s>s_{2}-s_{1}+q / T\)

Short answer

a) Δs = s2 - s1 b) Δs > s2 - s1 c) Δs < s2 - s1 d) Δs = q/T Answer: b) Δs > s2 - s1

Step-by-step solution

Understand the concept of entropy change

Entropy change (Δs) can be defined as the difference between the final entropy (s2) and the initial entropy (s1) of a substance.

Identify the given information

We are given: - Initial entropy s1 - Final entropy s2 - Heat gained q - Temperature T

Apply the concept of entropy change for irreversible processes

Since the process is irreversible, the entropy change of the substance (Δs) is always greater than the heat transfer divided by temperature (q/T). Mathematically, this can be written as: \[ \Delta s > \frac{q}{T} \]

Combine the equation for entropy change with the inequality

By combining the equation for entropy change and inequality, we have: \[ \Delta s > s_{2} - s_{1} \]

Compare and select the correct option

By analyzing the equation above, we can see that it matches option (b): \[ \Delta s > s_{2} - s_{1} \] So the correct answer is option (b) Δs > s2 - s1.

Key concepts

Thermodynamics

Thermodynamics is a branch of physics that deals with the relationships between heat, work, and other forms of energy. In essence, it is the study of energy transformations and how energy affects matter at the macroscopic level.

One of the fundamental principles of thermodynamics is the conservation of energy, which states that energy cannot be created or destroyed but can only change from one form to another. This principle lays the foundation for understanding how energy transfer takes place, whether it's in a steam engine, a refrigerator, or within biological systems.

It's essential to grasp that thermodynamics involves various laws and concepts which govern the behavior of systems at thermal equilibrium. These laws are useful for engineers, chemists, biologists, and even economists when they model energy usage in their respective fields.

Entropy

Entropy, symbolized by 's', is a measure of randomness or disorder within a system. The second law of thermodynamics states that the total entropy of an isolated system always increases over time. Entropy can also be viewed as a measure of energy dispersal.

When discussing entropy change, it's important to understand that it quantitatively represents the distribution of energy within a system and how much of that energy is unavailable to do work. In any process, the change in entropy (\( \text{d}s \)) is calculated by considering the initial and final states of the system. For reversible processes, the change in entropy is equal to the heat transfer divided by the temperature (\( \frac{q}{T} \)), but in irreversible processes, this is no longer strictly true due to additional entropy being produced within the system.

Heat Transfer

Heat transfer is the process by which thermal energy moves from one place to another. This can occur in three principal ways: conduction, which happens through direct contact; convection, which involves the movement of a fluid; and radiation, which involves energy being emitted through space.

In thermodynamics, when heat is added to a system, it can result in a temperature increase or a phase change. Understanding heat transfer is crucial for various applications, including designing heating and cooling systems, preventing heat loss in buildings, and improving the efficiency of engines and power plants.

Irreversible Processes

Irreversible processes are those that cannot return to their original state without leaving changes in the surroundings. They differ from reversible processes, which can be reversed without any change in both the system and environment.

Most natural processes are irreversible due to factors such as friction, turbulence, or spontaneous chemical reactions. In the case of irreversible processes, additional entropy is produced, making the entropy increase of the universe larger than in the case of reversible processes. This is critical to consider in engineering and environmental science when predicting the efficiency of a process or the impact of energy transformations on the surroundings.