Question

State the second law of thermodynamics. According to this law, what formula gives the maximum fraction of heat that can be transformed into electricity?

Short answer

The second law of thermodynamics states that entropy always increases, limiting efficiency. The maximum efficiency is given by Carnot's formula: \( \eta_c = 1 - \frac{T_c}{T_h} \).

Step-by-step solution

Understanding the Second Law

The second law of thermodynamics states that in any energy transfer or transformation, the total entropy of a system and its surroundings always increases. Entropy is a measure of disorder or randomness. It also means that no process is 100% efficient, and some energy will always be lost as waste heat.

Introduction to Heat Engines

The second law of thermodynamics also informs us about the limitations of heat engines, devices that convert heat energy into work or electricity. The law implies that not all heat energy can be converted into work; some must always remain as dissipated heat.

Maximum Efficiency Formula

The maximum efficiency (tac) of a heat engine operating between two heat reservoirs can be determined by the Carnot efficiency formula: \[ \eta_c = 1 - \frac{T_c}{T_h} \]where \( T_h \) is the absolute temperature of the hot reservoir and \( T_c \) is the absolute temperature of the cold reservoir.

Applying the Efficiency Formula

According to the second law, this Carnot efficiency formula gives the maximum possible fraction of input heat energy, \( Q_h \), that can be converted into work. This is important because real engines can never reach this efficiency due to practical limitations.

Key concepts

Understanding Entropy

Entropy is a fundamental concept in thermodynamics that represents the level of disorder or randomness within a system. Imagine a tidy classroom where everything has its place—entropy in this scenario is low. Now imagine that room after a 'free-for-all' chaotic event; entropy is much higher due to increased disorder.
As per the second law of thermodynamics, energy transformations increase the total entropy of a system and its environment. This is crucial because it explains why some energy is always lost as waste heat during energy transfers.
The idea of entropy is not just academic; it impacts how we think about energy efficiency and sustainability in all technological applications.

The Role of Heat Engines

Heat engines are devices that convert thermal energy into mechanical work or electricity. Examples of these include steam engines, car engines, and power plants.
According to the second law of thermodynamics, these engines can never convert all input heat into work because some energy must remain as waste heat, increasing the system's entropy.
This inherent limitation makes the design of heat engines all about maximizing efficiency while accepting that some energy will always contribute to environmental entropy.

Understanding the Carnot Efficiency Formula

The Carnot efficiency formula provides a theoretical maximum efficiency for a heat engine operating between two temperature reservoirs. It is given by the equation: \[ \eta_c = 1 - \frac{T_c}{T_h} \] Here, \( T_h \) is the absolute temperature of the hot reservoir, and \( T_c \) is the absolute temperature of the cold reservoir.
This formula helps us understand the limits of how well we can convert heat into work. It's critical to notice that no real engine can be perfectly efficient, as they are all bound to operate below this theoretical limit.

Key Aspects of Energy Transfer

Energy transfer is a core concept in thermodynamics involving the movement of energy from one form or location to another.
In the context of heat engines, energy transfer happens when thermal energy is converted to mechanical work. However, due to increased entropy, not all energy can be transferred usefully.
To design efficient systems, engineers must carefully manage these energy transfers, minimizing the waste heat that is inevitable due to the second law's stipulations.

Thermodynamic Efficiency Explained

Thermodynamic efficiency refers to the measure of how well an energy conversion or process converts input energy into useful work.
It considers the unavoidable increase in entropy during any energy transfer. Understanding this concept is key because it delves into which parts of the energy input can be transformed and which parts are lost.
The Carnot efficiency formula offers guidance on the theoretical limits of efficiency, but real-world systems must address practical challenges like friction, material constraints, and heat loss that lower the actual efficiency.