Boiler: Energy generation and Energy supply

Three questions have been answered in this post

-What does a boiler produce and supply, heat, or work?

-Does a boiler generate entropy?

-Can internal energy and work energy be separately estimated?

What does a boiler generate: Heat or Work?

The boiler generates and supplies enthalpy. It is expressed as H = U + W, H is enthalpy, U is internal energy and W is work energy. The internal energy consists of the kinetic and potential energy. Work is the PV [thermodynamic] component of the total energy H, which arises from the expansion of steam on the phase boundary line when water changes phase into vapor.

A boiler's efficiency is expressed as

E= [Q (H-h)/q x GCV] x100

Where,

Q= Quantity of steam generated (kg/hr)

q = Quantity of fuel (kg/hr)

H= Enthalpy of steam (Kcal/kg)

h= Enthalpy of water (kcal/kg)

GCV= Gross calorific value of the fuel.

The boiler's efficiency is a ratio of[ enthalpy out / enthalpy in] x 100

The internal energy and work energy are inseparable except for adiabatic processes which filter out the work energy while retaining the heat energy inside the system. In a boiler, when there is phase change the heat goes to increase both its internal energy and work energy arising from the expansion of steam as intermolecular bonds break.

Energy generation in the boiler

Explanation

The energy generation and consumption in a boiler can be best explained by a steam table. Focus [100 degc] on the 1st row of the steam table below. The data in the table is copy pasted from a steam table. There are two reference points used in the table, the start point is 0 degc and the endpoint is 100 degc. Pressure is constant at 1 bar.

The internal energy of water in the boiler at 100 degc

Refer to 5th column

This is the internal energy of saturated water, uf at 100 degc

The 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

Since water is incompressible, for water, the internal energy and enthalpy are the same.

This is the energy the saturated water carries at 100 degc/1 bar in the boiler

Expansion of volume and thermodynamic PV work

Refer to 3rd and 4th column

3rd column

The volume of water at 100 degc

The density of water at 100 degc= 958.05 kg/m3

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

4th column

The volume of steam at 100 degc

Density of steam at 100 degc =0.6 kg m^-3

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

Expansion of volume [ the difference between the specific volume of the saturated vapor and saturated liquid], (vg - vf) = [1.670-0.001043] = 1.6689 m3/kg

This expansion needs energy and that accounts for the work energy.

Enthalpy of saturated steam at 100 degc/1 bar

Refer to 8th column

The enthalpy of vaporization of water is 2256 kJ/kg in the boiler as water converts to steam at 100 degc/1 bar pressure.

This includes the internal energy of steam and the PV thermodynamic work. This is the latent heat that the steam transfers during heat transfer.

Total enthalpy of steam

Refer to 9th column

This shows the total energy carried by steam as it leaves the boiler

419 [ enthalpy of water at 100 degc] + 2256 [enthalpy of steam at 100 degc] = 2675 kJ/kg

Energy supply by steam

Energy supply by the steam is exactly a reverse phenomenon of steam acquiring energy.

The saturated steam with total energy 2675 kJ/kg during the transfer of energy condenses exothermically releasing the latent heat 2256 kJ/kg at the phase change point leaving hot water with an enthalpy of 419 kJ/g.

Energy transfer by steam to power plant turbine

A turbine typically works between a boiler that supplies enthalpy at the operating pressure and a condenser at constant pressure. The job of a condenser is to cool exhaust steam at the condenser pressure and temperature into saturated water [corresponding to the pressure and temperature] in the condenser. This water is usually reused along with feed water. The heat of condensation is sent to the cooling tower by the circulating water to reject the energy.

The difference in the enthalpy in H1 and enthalpy out H2, [H1-H2] runs the turbine.

Does a boiler generate entropy?

The answer is yes. However, it does not figure in the efficiency calculation. As a convention, the steam tables show the entropy generation separately. The entropy losses are part of exergy losses in a boiler.

Please refer to 10, 11 and 12 rows in the stable

Column 10

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

Column11

sfg, the entropy of saturated water-steam in equilibrium

Calculation

Sfg = hfg/T = 2256.4/373.15 = 6.0495 kJ/kg/k

Column 12

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

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

Can internal energy and work energy be separately estimated?

Yes, it can be estimated. For ideal gases, Cp dT - Cv dT = R dT

Cp symbolizes the specific heat at constant pressure and Cv is the specific heat at constant volume. Cp = dH/dT [ H is enthalpy, T is temperature]

Therefore dH = Cp dT

H represents Internal energy + Work

Thus Cp dT represents the total energy [ internal energy + Work]

Cv =dU/dT [U is internal energy]

dU = Cv dT,

Cv dT represents internal energy

Cp dT - Cv dT, represents work.

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