Tru Physics

Adiabatic Process

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Introduction

An adiabatic process in thermodynamics is one in which no heat is exchanged between a system and its surroundings. The word “adiabatic” comes from Greek roots meaning “impassable,” referring to the heat transfer. This concept is of paramount importance in the study of thermodynamics, heat engines, and atmospheric physics.

Adiabatic Condition

The condition for an adiabatic process is given by:

Q = 0

where Q is the heat transferred. In an adiabatic process, any change in internal energy U of the system is solely due to work done W on or by the system:

\Delta U = W

Adiabatic Process in an Ideal Gas

For an ideal gas undergoing an adiabatic process, the relationship between the pressure P and volume V is given by:

PV^\gamma = \text{constant}

where \gamma is the heat capacity ratio, defined as the ratio of the heat capacity at constant pressure C_p to the heat capacity at constant volume C_v. In relation to the number of degrees of freedom (f) available, \gamma can be expressed as:

\gamma = \dfrac{f+2}{f}.

There are several other important relationships for adiabatic processes:

VT^{f/2} = \text{constant}'

TV^{\gamma -1} = \text{constant}''

T^{\gamma}P^{1-\gamma} = \text{constant}'''

where T is temperature and the ' symbol is used to show that the constants in each equation are not equal to each other.

Adiabatic Cooling and Heating

An important implication of the adiabatic process is the concept of adiabatic cooling and heating. When a gas expands adiabatically (without adding heat), the gas does work on its surroundings and its internal energy decreases, leading to a decrease in temperature. This is adiabatic cooling. Conversely, when a gas is compressed adiabatically, work is done on the gas, increasing its internal energy and temperature, which is adiabatic heating.

Adiabatic process heating via volume compression.
Adiabatic heating via volume compression. The two lighter lines leading to the initial and final temperatures are isotherms (constant temperature). The solid dark line is called an adiabat.

Applications

Adiabatic processes are fundamental to the operation of many thermodynamic systems. They are central to the operation of heat engines, including internal combustion engines and Carnot engines. In atmospheric physics, adiabatic processes explain the temperature changes of rising and descending air parcels, crucial for understanding weather and climate.

Quantum Adiabatic Process

In quantum mechanics, the term adiabatic process is used in a different but related sense, referring to a system that evolves without sudden changes, allowing it to remain in its instantaneous eigenstate. This concept is central to adiabatic quantum computation and quantum annealing.

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