Processes of Vapours | Thermodynamics

The basic energy relations for the processes as defined for perfect gases also hold for vapours all previous equations in terms of the general symbols W, Q, H, h, U, u, K, P apply to any substance under the circumstances specified. The equations derived from the assumption of an ideal gas do not hold.

Remember that the areas on the P-V diagram under the curve at an internally reversible process represent ʃp.dv, and that this area is the work of a non-flow process. The area behind the same curve is the –ʃv.dp.

The vapour processes that are to be studied here are: 1. Constant Pressure Process 2. Constant Volume Process 3. Reversible Adiabatic Process (Isentropic Process) 4. Irreversible Adiabatic or Throttling Process 5. Isothermal Process 6. Polytrophic Process 7. Hyperbolic Process 8. Free Expansion.

1. Constant Pressure Process:

A constant pressure, also called an isobaric process, is a change of state during which the pressure remains constant. On the P–V plane, the process is represented by a horizontal line, and on the T-S plane the process is represented by a horizontal line in the wet region and by a curve obtained from the indefinite integral of –

ds = δq/T

In addition to defining relation, such as p = c, other quantities defining the limits of the process are needed. Suppose, in this case that point 1 is in the wet region and point 2 in the superheat region. With the pressure known, a point in the wet region is generally defined by giving its quality x or percentage moisture y. Similarly, a point 2 in the superheat region is generally, but not necessarily, defined by giving its temperature. The work of reversible non-flow process at p = c is –

2. Constant Volume Process:

A constant volume process, also called an isometric process is a change of state during which the volume remains constant. This process is represented by a vertical line 1- 2 in Fig. 10.12.

For non-flow, constant volume process we have –

3. Reversible Adiabatic Process (Isentropic Process):

Reversible adiabatic process is that process during which heat exchange is not taking place and Q = 0. This process is also called Isentropic process during which heat is zero and entropy change is also zero i.e., ΔS = 0.

This process is represented on PV plane, 1-2 Isentropic Compression, 3-4 Isentropic expansion and T-S plane of Fig. 10.13.

The isentropic and irreversible adiabatic can either be non-flow or steady flow. Let the second state along isentropic be designated along an irreversible adiabatic 2′.

Then, from the non-flow energy equations with Q = 0 for isentropic process, we write Q = ΔU + W_nf

∴ 0 = ΔU+ W_nf or W_nf = U₁ – U₂ or W = U₁ – U₂ (Reversible) and W = U₁ – U₂ (Irreversible)

For steady flow process we get, in general,

W = (h₃ – h₄) when ΔK = 0 (Reversible)

or W = h₃ – h₄ when ΔK = 0 (Irreversible)

An example of steady flow to which this equation applies is a steam turbine. If the process reversible (Isentropic), S₁ = S₂ = (S_f + xS_fg)₂ (Reversible non-flow or steady flow)

In which it is presumed that state 2 is in the wet region.

4. Irreversible Adiabatic or Throttling Process:

This term is generally reversed for an irreversible steady flow process, but the kinetic energies are not necessarily zero. This adiabatic process (Q = 0) occur from the extreme of no work being done, called a throttling process. This is a simple flow process with work W= 0. For an ideal gas, this throttling process is at constant temperature process, therefore when W = 0, ΔP = 0 and Q = 0, the energy equation is –

If velocity changes are negligible, then K₁ = K₂ and h₁ = h₂. This is a constant enthalpy process or Isenthalpic Process.

Thus the throttling process is defined by h₁ – h₂ and it is commonly used in steam power practice to determine the quantity of steam (dryness fraction of steam). Generally this process is shown by a dotted line on T-S plane as shown in Fig. 10.14 and by a vertical line on h-s diagram of Fig. 10.15.

5. Isothermal Process:

An Isothermal process is one carried out at constant temperature T = C. Unless stated otherwise, always it will be taken as a reversible process. For an ideal gas with T = C, we think immediately of Boyle’s Law, PV = Constant or P₁V₁ = P₂V₂. For steam, an ‘internally reversible’ isothermal process from a point in the superheat region to a point in the wet region is pictured in Fig. 10.16.

6. Polytrophic Process:

 

7. Hyperbolic Process:

When a gas or steam expands or is compressed in such a manner that the product of pressure and volume remains constant during the process of expansion or compression, the process is known as hyperbolic process because such a process on the P-V diagram will give a rectangular hyperbola. Hence a hyper­bolic expansion or compression process follows the law,

Pressure x Volume = Constant

P V = Constant

Note:

Remember we will have to calculate h₁, U₁ etc. at the condition of steam before the process commences.

8. Free Expansion:

When a fluid is allowed to expand suddenly into a vacuum chamber through an orifice of large dimensions, the free expansion of the fluid occurs. During this operation no heat has been supplied or rejected and no external work has been done; hence it follows that the total enthalpy of the fluid remains constant. This type of expansion is also called the constant total heat expansion.

After studying the different vapour process, we can conclude that for any process, it will be required to deter­mine or calculate –

(i) Heat during the process (Q)

(ii) Change in Internal energy (ΔU)

(iii) Change in Enthalpy (ΔH)

(iv) Work done (W)

(v) ʃ p.dV

(vi) – ʃ V.dP

(vii) Change in entropy (ΔS)