Thermodynamics (Laws, Heat Transfer)

Introduction to Thermodynamics

Thermodynamics is the branch of physics that deals with the study of heat, work, and the forms of energy. It explores how energy is transferred between systems and the laws governing these processes. Thermodynamics is fundamental to understanding the behavior of systems, from engines and refrigerators to biological systems.

Key Concepts in Thermodynamics

1. System and Surroundings: A system refers to the part of the universe being studied, while the surroundings are everything else outside the system.
2. State Variables: These are properties that describe the state of a system, such as pressure ($P$), temperature ($T$), volume ($V$), and internal energy ($U$).
3. Processes: Thermodynamic processes include isothermal, adiabatic, isobaric, and isochoric processes, each involving changes in temperature, pressure, or volume under specific conditions.

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Laws of Thermodynamics

First Law of Thermodynamics (Law of Energy Conservation)

The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed. In mathematical form, it is represented as:

$\mathrm{\Delta }U=Q–W$

Where:

• $\mathrm{\Delta }U$ is the change in internal energy of the system.
• $Q$ is the heat added to the system.
• $W$ is the work done by the system.

This law explains how energy is conserved in all processes, whether the system is gaining or losing heat or doing work.

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Second Law of Thermodynamics

The second law of thermodynamics states that in any energy transfer, some energy becomes unavailable to do useful work, and the total entropy of an isolated system always increases over time. Entropy is a measure of disorder in a system.

The second law can be expressed as:

$\mathrm{\Delta }S\ge 0$

Where:

• $\mathrm{\Delta }S$ is the change in entropy.

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Third Law of Thermodynamics

The third law of thermodynamics states that as the temperature of a system approaches absolute zero, the entropy of a perfect crystal approaches zero. In other words, it is impossible to reach absolute zero in a finite number of processes.

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Zeroth Law of Thermodynamics

The zeroth law states that if two systems are each in thermal equilibrium with a third system, then they are in thermal equilibrium with each other. This law allows us to define temperature in a meaningful way.

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Heat Transfer Mechanisms

Heat transfer is the process by which thermal energy is exchanged between physical systems due to a temperature difference. The three main modes of heat transfer are:

1. Conduction: The transfer of heat through a material without the movement of the material itself. The rate of heat conduction is given by Fourier’s law:$Q=-kA\frac{dT}{dx}$Where:
   • $Q$ is the rate of heat transfer.
   • $k$ is the thermal conductivity of the material.
   • $A$ is the cross-sectional area through which heat is transferred.
   • $dT/dx$ is the temperature gradient.
2. Convection: The transfer of heat by the movement of a fluid (liquid or gas). The rate of heat transfer by convection can be described as:$Q=hA(T_s–T_f)$Where:
   • $h$ is the heat transfer coefficient.
   • $A$ is the surface area.
   • $T_s$ is the surface temperature.
   • $T_f$ is the fluid temperature.
3. Radiation: The transfer of heat in the form of electromagnetic waves, such as infrared radiation. Stefan-Boltzmann law gives the rate of radiative heat transfer:$Q=\sigma A{T}^4$Where:
   • $\sigma$ is the Stefan-Boltzmann constant.
   • $A$ is the surface area.
   • $T$ is the absolute temperature of the radiating body.

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Examples

Example 1: First Law of Thermodynamics Application

Question: A gas absorbs $500,J$ of heat and does $200,J$ of work. What is the change in internal energy of the gas?

Answer:

Step 1: Given Data:

• Heat added to the system, $Q=500,J$
• Work done by the system, $W=200,J$

Step 2: Solution: Using the first law of thermodynamics: $\mathrm{\Delta }U=Q–W$

Substitute the given values: $\mathrm{\Delta }U=500,J–200,J$

Step 3: Final Answer: $\mathrm{\Delta }U=300,J$

The change in internal energy of the gas is $300,J$.

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Example 2: Heat Transfer by Conduction

Question: Calculate the heat conducted through a metal rod of length $0.5,m$, cross-sectional area $0.01,m^2$, and thermal conductivity $50,W/mK$ if the temperature difference across the rod is $100,K$.

Answer:

Step 1: Given Data:

• Length, $L=0.5,m$
• Cross-sectional area, $A=0.01,m^2$
• Thermal conductivity, $k=50,W/mK$
• Temperature difference, $\mathrm{\Delta }T=100,K$

Step 2: Solution: Using Fourier’s law for conduction: $Q=-kA\frac{\mathrm{\Delta }T}{L}$

Substitute the values: $Q=-(50)(0.01)\frac{100}{0.5}$

$Q=-50,W$

Step 3: Final Answer: The heat conducted through the rod is $50,W$.

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Applications of Thermodynamics

1. In Engines: Thermodynamic principles are applied in designing internal combustion engines, jet engines, and refrigeration systems.
2. In Power Plants: Thermodynamics is used to convert heat energy into electrical energy in thermal power plants.
3. In HVAC Systems: Thermodynamics principles are critical in heating, ventilation, and air conditioning systems.
4. In Space Science: Thermodynamics governs the behavior of gases in space and the transfer of energy in space missions.

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Frequently Asked Questions (FAQs)

1. What is the first law of thermodynamics?
   • Answer: The first law of thermodynamics is the law of energy conservation, stating that energy can neither be created nor destroyed, only transferred or transformed.
2. How is heat transferred by conduction?
   • Answer: Heat is transferred by conduction through direct contact between molecules, with energy flowing from the hotter to the cooler area.
3. What is entropy in thermodynamics?
   • Answer: Entropy is a measure of disorder or randomness in a system, and according to the second law of thermodynamics, the entropy of an isolated system always increases.
4. What are the units of heat transfer?
   • Answer: The SI unit of heat transfer is the joule (J). Other units include calories and BTUs (British Thermal Units).
5. How does the third law of thermodynamics apply in real life?
   • Answer: The third law of thermodynamics indicates that absolute zero is unattainable, and as systems cool down, their entropy decreases.