Polytropic Process Equations

September 19, 2024 Post a Comment

Polytropic process equations

We study the primordial Universe in a cosmological model where inflation is driven by a fluid with a polytropic equation of state p = \alpha\rho + k\rho^{1 + 1/n}. We calculate the dynamics of the scalar factor and build a Universe with constant density at the origin.

How do you derive the equation of polytropic process?

Hint:We have to know that a polytropic process is a thermodynamic process which follows the relationship: $p{V^n} = C$ . Here p represents pressure, V represents volume and n is the polytropic index, and C represents constant.

How do you calculate n for a polytropic process?

In a polytropic process, P V^n = constant.
If a relation in T and V is given, then you can use ideal gas equation and put T= PV/R and find n.
for eg, if TV = constant,
then P^2 V = constant.
taking square root, we get P V^1/2 = constant.
thus n= 1/2.
to find C for the process,
C = Cv + R/(1-n)

What is polytropic process example?

An example of a polytropic process is the expansion of the combustion gasses in the cylinder of a water-cooled reciprocating engine.

What is K in polytropic process?

Here k is the ratio of the specific heat at constant pressure, CP, to specific heat at constant volume, CV. The specific heats will be discussed later.

What is polytropic model?

Polytropic models represent stars in hydrostatic equilibrium that follow the polytropic equation of state, P=Kρ(n+1)/n. for piecewise-constant K and polytropic index n. The formalism behind these models is described in the Composite Polytropes section.

Is a polytropic process adiabatic?

Hence, to hold PV constant in the polytropic gas expansion/compression process, both heat and work interchange takes place between the system and surrounding. Therefore, polytropic is a non-adiabatic process.

What is polytropic process for ideal gas?

A polytropic process for an ideal gas is represented by equation = PV^n constant. If gamma is ratio of specific heats (Cp/Cv) . then value of n for which molar heat capacity of the process is negative, is given as.

Is Isochoric process polytropic?

Since the volume remains constant, the heat transfer into or out of the system does not the p∆V work but only changes the system's internal energy (the temperature). The case n ➝ ∞ corresponds to an isochoric (constant-volume) process for an ideal gas and a polytropic process.

What is the value of n in PV n C?

That means temperature of the gas remains constant given that the process is reversible and ideal. That means reversible isenthalpic process is nothing but a reversible isothermal process. So the value of n will be 1.

What does polytropic process becomes if value of index n 1?

Ans: In a polytropic process where PVn =constant, the temperature remains constant only when the polytropic index n = 1. For n = 1: PV = C: Under the Assumption of Ideal Gas Law, The PV = C represents the Constant Temperature or Isothermal Process.

Is a polytropic process isothermal?

Isothermal process are a subset of the polytropic. Polytropic encompass all other common processes and more. standard notation implying C is a constant, P the pressure and V the volume.

Is isobaric a polytropic process?

The isobaric, isothermal, isentropic and isochoric processes are therefore only to be regarded as special cases of a generally polytropic process!

Is entropy constant in polytropic process?

These are processes in which a state variable—volume, pressure, temperature, or entropy— remains constant. It turns out that these four processes are examples of a more general ideal-gas process, called a polytropic process, in which the specific heat remains constant.

How do you calculate heat transfer in polytropic?

1. This equation can be write like this m r into. This d t as t 2 minus t 1 plus p 1 v 1 minus p 2 v

Why is CV and CP important?

Cp is the term used to define the molar heat capacity of a substance when the pressure is constant, whereas Cv is the term used to indicate the molar heat capacity of a substance when the volume is constant. As a result, the molar heat capacity is defined by these two factors when pressure and temperature are varied.

What is a polytropic expansion?

A process which occurs with an interchange of both heat and work between the system and its surroundings. Nonadiabatic expansion or compression of a fluid is an example of a polytropic process.

What is the value of polytropic index?

Most practical thermodynamic processes can be considered polytropic with values ranging between the theoretical limits of 1 and 1.4. The value can also be considered as defining the gradient of the compression and expansion lines on a logarithmic pressure/volume diagram.

What is polytropic efficiency?

The polytropic efficiency—also called “small-stage efficiency”—is defined as the isentropic efficiency of an elemental (or differential) stage in the process such that it is constant throughout the whole process.

Are polytropic processes reversible?

The term "polytropic" was originally coined to describe any reversible process on any open or closed system of gas or vapor which involves both heat and work transfer, such that a specified combination of properties were maintained constant throughout the process.