Question

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.