The relation between volume (V) and absolute temperature (T) of a gas in an adiabatic process is:
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In adiabatic processes, the product of the temperature and volume raised to the power \( \gamma - 1 \) is constant, where \( \gamma \) is the adiabatic index. This relationship is important in thermodynamics for processes where no heat is exchanged with the surroundings.
In an adiabatic process, there is no heat exchange with the surroundings, and the relation between the pressure, volume, and temperature of a gas is governed by the following equation:
\[
TV^{\gamma - 1} = \text{constant}
\]
Where:
- \( T \) is the absolute temperature,
- \( V \) is the volume,
- \( \gamma \) is the adiabatic index (ratio of specific heats \( C_p / C_v \)).
This equation states that in an adiabatic process, the product of the temperature and volume raised to the power of \( \gamma - 1 \) is constant.
Thus, the correct relation between volume and temperature for an adiabatic process is:
\[
\boxed{TV^{\gamma - 1} = \text{constant}}
\]
