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# Thermodynamics

Thermodynamics is a branch of Physics which deals with the equilibrium, energy and its transformation from one form to another. It deals with the relationships between heat and work, and the properties of the system in equilibrium. Historically, Thermodynamics originated as a result of man's endeavor to convert heat into work. The principles of thermodynamics are summarized in the form of four laws that fall within the constraints implied by each which are zeroth law of thermodynamics, first law of thermodynamics, second law of thermodynamics and third law of thermodynamics.
Thermodynamics studies the behavior of Energy. Energy exists in many forms, such as heat, light, electrical energy, chemical energy etc. Energy is the ability to bring about change or to do work. It deals with various macroscopic variables like pressure, temperature, internal energy etc. The results of thermodynamics are useful for other branches and fields of physics and engineering like mechanical, chemical, physical, biomedical, geology, psychrometrics, statistics etc.
Thermodynamics is the study of Heat and Thermal energy.  It is a science which studies various interactions amongst energy, heat, work and temperature, with matter that brings about significant changes in the macroscopic properties of a substance that are measurable. It is basically a phenomenological science based on certain laws of nature which are always obeyed and never seen to be violated.

## What is Thermodynamics?

Thermodynamics is a macroscopic science which studies various interactions amongst energy, notably heat and work transfer, with matter that brings about significant changes in the macroscopic properties of a substance that are measurable. The laws of thermodynamics dictate energy behavior, for example, sweating in a crowded room, taking a bath, melting ice cube etc.

## Laws of Thermodynamics

These are the basic laws of thermodynamics :
1. Zeroth law of thermodynamics
2. First law of thermodynamics
3. Second law of thermodynamics
4. Third law of thermodynamics

## Thermodynamics Equations

The most fundamental equation of thermodynamics is:

$P$ = $\frac {W}{t}$

Here, P = power, W = work, t = time
Hence,
$P$ = $\frac {mgH}{t}$

The fundamental equations of thermodynamics are first and second law of thermodynamics. Both of them are combined to form a common thermodynamic relation.

$dU = TdS – pdv + \sum_{i=1}^{k}u(i)dN(i)$

There are K+2 dimensions for thermodynamics space. U, S, V and N are the extensive quantities. The connections between the state variables are called equation of thermodynamic state. When the system reaches the state of thermal equilibrium then it is described with certain measurable variables that are called state variables. For example for ideal gas we write, $PV = nRT$

## Thermodynamics Examples

1. The Evaporation of sweat from your body is an example of thermal equilibrium in action.
Solution A:
System : The sweat
Surroundings :Your body + the rest of the universe
q > 0 so, Heat flows into the system (sweat) from you in order to raise the kinetic energy of the sweat molecules enough to allow them to go from the liquid phase to the gas phase.
Solution B
System: You
Surroundings: The sweat + the rest of the universe
q < 0 : Heat flows out of the system (you) into the sweat.
Since heat leaves your body this cools you down. This is the reason for our sweating.
2. Let us consider two glasses full of water. For one glass, the temperature of water is above the normal room temperature, and for the other glass it is below the normal room temperature. They are left on the table for some time such that they both are not in contact with each other. If you check the glasses after some time, both the glasses reach equilibrium. As observed, both the glasses of water are at the same temperature. The two glasses actually come in contact with the thermal equilibrium with the surroundings. Hence, they are in thermal equilibrium with each other also and they are at the same temperature.

An adiabatic process is a Thermodynamic process in which no heat is gained or lost by the system. If the container of the system in which the process is taking place has thermally-insulated walls or the process completes in a very short time period, so that, there is no opportunity for significant heat exchange then we say an adiabatic process has occurred. Where, Q = 0.Applying the law of Thermodynamics to an adiabatic process we get dQ = 0. Since delta-U is the change in internal energy of the system and W is the work done by the system. Any process that occurs within a system that is a good thermal insulator is also adiabatic.

$dQ = dv + dw = 0, du = -dw$

$U_{2}-U_{1}$=$\Delta U$ = $\Delta - dW$ (Adiabatic process)

When a system expands adiabatically, dW is positive (the system does work on its surroundings), so $\Delta U$ is negative and the internal energy decreases. When a system is compressed adiabatically, dW is negative (work is done on the system by its surroundings) and $\Delta U$ increases. In many (but not all) systems, an increase of internal energy is accompanied by a rise in temperature. The compression stroke in an internal-combustion engine is almost an adiabatic process. The temperature rises as the air-fuel mixture in the cylinder is compressed. The expansion of the burned fuel during the power stroke is also nearly an adiabatic expansion with a drop in temperature.

## Isothermal Process

##### An Isothermal Process is a thermodynamic process in which the temperature of the system remains constant.  Where, $\Delta$ T= 0. For a process to be isothermal, any heat flow into or out of the system must occur slowly enough so that thermal equilibrium is maintained. In general, none of the quantities $\Delta$U, Q or dW is zero in an isothermal process. During an isothermal process there is a change in internal energy, work and heat. The heat transfer into or out of the system naturally must happen at such a slow rate that the thermal equilibrium is maintained.

A hypothetical setup for studying the behavior of gases

The pressure p, volume V, temperature T and number of moles of a gas can be controlled and measured using this setup.