In the polytropic process, equation pvn = constant, if n = 0, the process is called
(a) constant pressure (c) constant temperature
(b) constant volume (d) adiabatic
The correct answer and explanation is :
Correct Answer: (a) Constant Pressure
Explanation:
The polytropic process is represented by the equation:
[
p v^n = \text{constant}
]
where:
- ( p ) is pressure,
- ( v ) is volume,
- ( n ) is the polytropic index.
This equation describes many thermodynamic processes depending on the value of n. Each specific value of ( n ) corresponds to a different type of process:
- ( n = 0 ): Constant pressure
- ( n = 1 ): Isothermal (constant temperature)
- ( n = \gamma ) (where ( \gamma = C_p/C_v )): Adiabatic
- ( n \rightarrow \infty ): Constant volume
Why is it constant pressure when ( n = 0 )?
Let’s substitute ( n = 0 ) into the polytropic equation:
[
p v^0 = \text{constant} \Rightarrow p \cdot 1 = \text{constant} \Rightarrow p = \text{constant}
]
So, if ( n = 0 ), the equation simplifies to ( p = \text{constant} ), which means the pressure remains unchanged throughout the process — that is the definition of a constant pressure process, also known as an isobaric process.
Summary of Different n Values in Polytropic Process:
| Value of ( n ) | Type of Process | Equation Outcome |
|---|---|---|
| ( n = 0 ) | Constant Pressure (Isobaric) | ( p = \text{constant} ) |
| ( n = 1 ) | Constant Temperature (Isothermal) | ( pv = \text{constant} ) |
| ( n = \gamma ) | Adiabatic | ( p v^\gamma = \text{constant} ) |
| ( n \to \infty ) | Constant Volume (Isochoric) | ( v = \text{constant} ) |
Therefore, when ( n = 0 ) in the polytropic process equation, it represents a constant pressure process.
Correct Option: (a) Constant Pressure ✅
