A reversible polytrophic process can be described by the equation
Polytropic Process Equation Explained
A polytropic process is a thermodynamic process that can be described by the following equation relating pressure (P), volume (V), and a constant (C):
\(PV^n = C\)
In this equation:
- P represents the pressure of the system.
- V represents the volume of the system.
- n is known as the polytropic index or polytropic constant. It is a dimensionless number that characterizes the specific polytropic process.
- C is a constant for the process.
The value of the polytropic index n determines the nature of the process:
- If n = 0, the process is isobaric (constant pressure). The equation becomes P = C.
- If n = 1, the process is isothermal (constant temperature) for an ideal gas. The equation becomes PV = C.
- If n = \(\gamma\) (where \(\gamma\) is the ratio of specific heats, \(C_p/C_v\)), the process is adiabatic (no heat transfer). The equation becomes \(PV^\gamma = C\).
- If n approaches infinity, the process is isochoric (constant volume). The equation approaches V = C.
The question asks for the general equation that describes a reversible polytropic process. Based on thermodynamic principles, the standard and correct form is PVn = C.
Let's look at the options provided:
- Option 1: PVn = C - This matches the standard definition of a polytropic process.
- Option 2: (PV)n = C - This simplifies to PnVn = C, which is not the correct form.
- Option 3: \({\left( {\frac{P}{V}} \right)^n} = C\) - This simplifies to Pn / Vn = C or Pn = CVn, which is incorrect.
- Option 4: PnV = C - This is a different relationship and not the standard polytropic equation.
Therefore, the correct equation representing a reversible polytropic process is PVn = C.
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