An adiabatic process is a thermodynamic process in which no heat is exchanged with the surroundings. This means that any change in the internal energy of the system is solely due to work done on or by the system.
In an adiabatic process, the first law of thermodynamics can be expressed as:
\[ \Delta U = Q - W \]
where:
- \(\Delta U\) is the change in internal energy,
- \(Q\) is the heat exchanged (which is 0 in an adiabatic process), and
- \(W\) is the work done by the system.
Since \(Q = 0\) in an adiabatic process, the equation simplifies to:
\[ \Delta U = -W \]
This means that any work done on the system (compression) will increase its internal energy and any work done by the system (expansion) will decrease its internal energy.
For an ideal gas undergoing an adiabatic process, the relation between pressure (P), volume (V), and temperature (T) is given by the following equations:
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Adiabatic Condition: \[ PV^\gamma = \text{constant} \] where \(\gamma = \frac{C_p}{C_v}\) is the heat capacity ratio (specific heat at constant pressure \(C_p\) to specific heat at constant volume \(C_v\)).
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Temperature-Volume Relation: \[ TV^{\gamma - 1} = \text{constant} \]
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Temperature-Pressure Relation: \[ TP^{\frac{1 - \gamma}{\gamma}} = \text{constant} \]
These equations illustrate the relationship between pressure, volume, and temperature during an adiabatic change in an ideal gas.
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