Polytropic Process Characteristic for n=0

This question examines the nature of a polytropic process, defined by the equation $PV^n = C$, under a specific condition where the polytropic index $n$ is zero. Understanding the implications of $n=0$ is key to identifying the constant property.

Polytropic Equation Definition

The general form of a polytropic process is given by the relationship:

$PV^n = C$

where:

• $P$ represents pressure
• $V$ represents volume
• $n$ is the polytropic index
• $C$ is a constant

Derivation for n=0

We are given the condition that the polytropic index $n = 0$. Substituting this value into the polytropic equation yields:

$PV^0 = C$

Since any non-zero quantity raised to the power of zero equals 1 (i.e., $V^0 = 1$, assuming $V \neq 0$), the equation simplifies to:

$P \times 1 = C$

Which further simplifies to:

$P = C$

Resulting Constant Property

The derived equation $P = C$ indicates that the pressure ($P$) remains constant throughout the process. Therefore, a polytropic process with $n=0$ is characterized by constant pressure.

This specific case corresponds to an isobaric process.

Comparing this result with the given options, the correct characteristic is constant pressure.