Briefly explain the term Adiabatic process with the aid of equations

Answer 1

An adiabatic process is a thermodynamic process in which no heat is transferred to or from the system to its surroundings. As a result, the internal energy of the system changes due to work done on or by the system rather than heat exchange.

Key Characteristics:

1. No Heat Transfer: \( Q = 0 \)
2. Change in Internal Energy: The change in internal energy (\( \Delta U \)) is equal to the work done on or by the system (\( W \)). \[ \Delta U = W \]

For an Ideal Gas:

For an ideal gas undergoing an adiabatic process, we can use the following equations:

First Law of Thermodynamics: \[ \Delta U = Q - W \] Substituting \( Q = 0 \): \[ \Delta U = -W \]

Adiabatic Condition:

For an ideal gas, the relationship between pressure (P), volume (V), and temperature (T) during an adiabatic process can be expressed as: \[ PV^{\gamma} = \text{constant} \] where \( \gamma = \frac{C_p}{C_v} \) is the heat capacity ratio (with \( C_p \) being the heat capacity at constant pressure and \( C_v \) being the heat capacity at constant volume).

Temperature Relationship:

The temperatures and volumes are related by: \[ TV^{\gamma - 1} = \text{constant} \] And the temperatures and pressures are related as: \[ T^{\gamma} P^{1 - \gamma} = \text{constant} \]

These equations govern the behavior of ideal gases during adiabatic expansion or compression.