Dynamic equilibrium in steam making

At dynamic equilibrium in saturated steam, the rates of evaporation and condensation are equal, leading to a constant temperature phase change known as the saturation phase change. There is no separate accounting of heat for intermolecular bonds breaking in a dynamic equilibrium. This point is not often understood. ?

It is a simple note. The note describes how heat distributes between two phases steam and water. The note has been prepared by taking cue from the activities of steam when made from water by referring to two fundamental reference points [1] the pressure-enthalpy diagram of steam and [2] the steam table with understanding nothing can be more accurate than this.

Pressure-Enthalpy [P-H] diagram: Enthalpy and pressure are related by the most important equation of the first law of thermodynamics?H = U + PV. PdV is work. Positive work would increase internal energy and negative work would reduce internal energy. Therefore, this equation helps us understand the change in internal energy and its impact on enthalpy.

In the steam-making process [ image below] the enthalpy [total energy] increases at constant saturation pressure as water goes from its dryness fraction of zero to one. This is one single point, I guess describes the entire distribution of heat in steam-making involving various sub-processes and if this point is understood understanding steam-making becomes easy.

Pressure-Enthalpy diagram of steam

In the P-H diagram, the pressure is on the y-axis. Enthalpy is on the x-axis. On the left side of the dome, there is a water region. On the right side of the dome, there is a superheated steam region. Within the dome, there is a saturation region. The phase change of water to vapor takes place within this dome. Within the dome, the blue lines are temperature lines. The green lines appearing from the x-axis are the dryness fraction lines. These lines are showing the dryness of water vapor as you go from left to right in the dome as water is heated. The dotted lines within the dome parallel to the x-axis are enthalpy lines ?

The left outline of the dome represents saturated water and the right-side outline represents dry saturated steam.

The dome represents the saturated region of vapor and water as said earlier. The two phases achieve dynamic equilibrium within the dome. A dynamic equilibrium occurs when two reversible processes proceed at the same rate. The rate of evaporation equals the rate of condensation. ?Every particle of vapor and water is in thermal equilibrium with another inside the dome. Every particle of water and vapor inside the dome has the same internal energy and they are in thermal equilibrium. This further means that vapor and water are at the same temperature within the dome and there is no heat exchange between them.? There is confusion about how we define water-steam equilibrium. Water-steam equilibrium means water-steam thermal equilibrium. Water steam remains in thermal equilibrium within the dome as said above.

The P-H graph looks like a BELL. The width of the bell represents the?heat of vaporization?which gradually narrows and converts into a point with increasing pressure at the topmost point of the bell curve which is known as the critical point [red-dot].

Steam table:? A steam table provides the thermodynamic data to explain the properties of water or steam. Below, there is a steam table for saturated steam. It has twelve columns each representing a thermodynamic property of saturated steam. Please follow the row of 100 degc /0.1014Mpa [atmospheric pressure]

Steam-making process: How enthalpy changes at constant pressure

?[ Please follow the P-H diagram and the steam table]

Assume you have 1 kg water at 1 bar [100 kPa] pressure.

Reference columns 1 and 2 of the steam table

Let us heat the water [ reference columns 1 and 2 on the steam table and on the left corner of 100 degc/ 100 kPa line in the P-H diagram. 1 bar = 100 kPa].

Reference: 3rd column on the steam table

The density of water at 100 degc= 958.05 kg/m3 [the figure taken from the internet]

Specific volume of water, vf = 1/958.05 = 0.001043 m3/kg

Reference: 4th column on steam table

Density of steam at 100 degc =0.6 kg m^-3 [from internet]

Specific volume of steam, Vg = 1/0.6 = 1.670 m3/kg

Reference: 5th column on steam table

The internal energy of saturated water, uf at 100 degc

Internal energy of saturated water at 100 degc is its stored energy which is mass x specific heat x delta t. The specific heat of water at 0 degc, = 4.191 kJ/kg/k, ug = 1x 4.19x100 = 419.1kJ/kg. This is the sensible heat that water contributes at 100 deg.

Reference: 6th column on the steam table

ug, the internal energy of saturated steam

P= 0.1014 mPa, vg = 1.670 m3/kg]

1 mPa = 1000000 Newton/m2

0.1014 mPa = 1000000x 0.1014

PV= 1000000x 0.1014 x 1.670 = 169338 Newton-meter [PV = Work]

1kJ = 1000 Newton-meters

Therefore, PV = 169.338 KJ,

ug = hg – PV [ Comes from 1st law of thermodynamics, Enthalpy of steam, hg = Internal energy of steam +PV work]

hg = 2675.6 kJ/kg [ Important point: Here there is consumption of energy [endothermic] as H bonds break and water expands, this number comes from the P-H diagram. Refer to P-H diagram

ug = 2675.6-169.338 = 2506.3 KJ/kg

This is the internal energy change in steam as saturated water becomes saturated steam with a dryness fraction going from x=0 to x=1. Water. ??This is the heat of the vaporization of water. This represents the 100 degc / 100 kPa line as it goes from left to right in the P-H diagram.

Reference: 7th column on the steam table

hf, enthalpy of water,

Calculation

Since hf = uf + w and w [work] is zero for water, hf = uf, therefore,

hf = 419.1 kJ/kg

Reference: 8th column on the steam table

hfg, the enthalpy of saturated water-steam vapor inside the bell curve [ Reference; P-H diagram]

Calculation

hfg = hg-hf [ difference of enthalpy of saturated steam and enthalpy of saturated water on the saturated water line of PH diagram. [Refer to P-H diagram]

hfg = [2675.6-419.1] = 2256.5 kJ/kg

Reference: 9th column on the steam table

hg, the enthalpy of saturated steam. This is a property of water, 2675.6 KJ/kg at 100 degc and 0.1014 mPa pressure.?

hg = 2675.6 kJ/kg: this is the latent heat of steam. The number comes from P-H diagram

Entropy

As water converts to

Reference: 10th column on the steam table

?sf, the entropy of water

Calculation

Along with this sensible heat water also brings entropy Sf = Cp x ln T2/T1 [ T1 = 0+273.15= 273.15k] and [T2 = 100+273.15, T2/T1 = 373.15/273.15 =1.366]

Sf = Cp x ln 1.366 = 4.191x 0.312 = 1.30 kJ/kg/k

Sf = 1.3 kJ/kg/k

11th column on the steam table

sfg. The entropy of steam-water in equilibrium inside the bell curve

Calculation

Sfg = vfg/T = 2256.4/373.15 = 6.0495 kJ/kg/k [ it is simply Q/T of saturated steam]

12th column on steam table

sg, the entropy of saturated steam on the saturated steam line.

Calculation

It is the sum of sf + sfg [entropy of saturated water +entropy of water-steam in equilibrium]

sg = 1.3+6.0495 = 7.3495 Kj/kg/k

Energy distribution [ You can cross-check with the steam table]

Enthalpy of water = 419 kj/kg , Enthalpy of saturated steam= 2256.5 kJ/kg

Latent heat of water = 419+2256.5 = 2675.5 kj. There is no separate accounting of heat for intermolecular bonds breaking in a dynamic equilibrium. This point is not often understood. ?