Sunday, 14 Jul 2024
Technology

Calculation of Entropy Change

Entropy is a fundamental concept in thermodynamics that measures the disorder or randomness of a system. It plays a crucial role in understanding and analyzing various processes. In this article, we will explore the calculation of entropy change and its significance in different scenarios.

Entropy: A State Function

  1. Entropy is a state function. It means that the entropy change between two states depends only on their initial and final states, regardless of the path taken to reach those states.

  2. For reversible processes, entropy remains constant. It is an exact differential of a function that is identical to entropy itself.

Let’s dive deeper into some specific cases to understand how to calculate entropy change.

Absorption of Energy by a Constant Temperature Reservoir

Consider the scenario of adding energy to a constant temperature reservoir. This energy can be added either reversibly or irreversibly, either as heat or by performing work. Let’s look at an example to better grasp the concept.

Example:
The contents of a large constant-temperature reservoir, maintained at 500 K, are continuously stirred by a paddle wheel driven by a 250W electric motor for two hours. We want to estimate the entropy change of the reservoir.

To calculate the entropy change, we consider an imaginary reversible process with identical energy addition. This allows us to simplify the analysis and determine the entropy change of the reservoir between the initial and final states.

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Heating or Cooling of Matter

In this case, we focus on how entropy changes during the heating or cooling of a substance.

Example:
Consider heating 1kg of water from 300°C to 800°C at 1 bar pressure. The specific heat of water is 4.2 kJ/kg-K. We want to calculate the entropy change during this process.

Phase Change at Constant Temperature and Pressure

Phase changes, such as melting or boiling, also involve entropy changes. Let’s explore an example to understand the calculations involved.

Example:
Ice melts at 0°C with a latent heat of fusion of 339.92 kJ/kg. Water boils at atmospheric pressure at 100°C with a latent heat of vaporization of 2257 kJ/kg.

Adiabatic Mixing

Adiabatic mixing refers to the process of combining two substances without any heat exchange with the surroundings. Let’s take a look at an example to see how entropy change is calculated in such scenarios.

Example:
A lump of steel weighing 30kg at 427°C is dropped into 100kg of oil at 27°C. The specific heats of steel and oil are 0.5 kJ/kg-K and 3.0 kJ/kg-K, respectively. We want to calculate the entropy change of steel, oil, and the universe.

Frequently Asked Questions

Q: What is entropy?
A: Entropy measures the disorder or randomness of a system in the field of thermodynamics.

Q: Is entropy a state function?
A: Yes, entropy is a state function, meaning that its value only depends on the initial and final states of a system.

Q: How is entropy change calculated?
A: Entropy change is calculated by considering the initial and final states of a system and analyzing the specific process or scenario.

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Conclusion

Entropy change is a fundamental concept in thermodynamics that allows us to understand and analyze various processes. By calculating the entropy change, we can gain insights into the behavior of systems undergoing energy transfer or phase change. Understanding entropy change is crucial for engineers and scientists in the field of thermodynamics.

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