Specific Enthalpy: 25 Interesting Facts To Know

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Specific Enthalpy definition

Specific enthalpy is the measure of the total energy of a unit mass. It is defined as the sum of specific internal energy and flow work across the boundary of the system.

Units of Specific Enthalpy

The unit of specific enthalpy (h) is kJ/kg.

Specific Enthalpy equation

The equation of specific enthalpy is

h = u + Pv

Where,

h = Specific Enthalpy  

u = Specific Internal Energy

P = Pressure of the system

v = Specific volume of the system

Specific Enthalpy formula

h = u+Pv

h = cp (dT)

Where,

cp= specific heat capacity

dT = Temperature difference

Specific Enthalpy of dry air

It is defined as the product of the specific heat capacity of air at constant pressure and dry bulb temperature

h = cp (T)

Cp: Specific heat of air at constant pressure

Cp(AIR) : 1.005 kJ/kg-K

T: Dry Bulb Temperature

Specific Enthalpy of ethanol

The specific enthalpy of ethanol (C2H5OH) is 2.46 J/g℃

Specific Enthalpy of water at different temperatures

Specific enthalpy of water (hwater) is given by the product of the specific heat capacity of water Cwater and  the temperature. At ambient conditions (Pressure 1 bar), water boils at 100℃, and the specific enthalpy of water is 418 KJ/Kg.

Cwater = 4.18 kJ/kg K

Specific enthalpy of liquid water at atmospheric pressure under condition and different temperature has been illustrated below:

specific enthalpy
Fig 1: specific enthalpy of liquid water vs. Temperature

Enthalpy equation specific heat

Enthalpy is defined as the total energy content of a system. It is expressed as product of mass, specific heat and change in temperature of system.

H = m Cp (Tf – Ti)

Where,

H = enthalpy

Cp =specific heat capacity at constant pressure

m = mass of the system

Ti = Initial temperature

Tf = final temperature

Specific Enthalpy of air

It is defined as the summation of specific enthalpy of dry air and specific enthalpy of moist air.

h = 1.005*t+ω (2500+1.88 t)

h = enthalpy of moist air kJ/kg

t = Dry Bulb Temperature in ℃

ω = specific humidity or humidity ratio in kg/kg of dry air

Specific humidity is defined as the ratio of the mass of water vapour per Kg of dry air in a given volume and given temperature.

Specific enthalpy of air table

Variation of thermodynamic properties of air with respect to temperature at atmospheric pressure condition have been provided below.

Screenshot 2021 05 11 at 6.54.19 AM
Fig 2: Thermodynamic property of liquid gas (image credit :thermopedia)

Specific Enthalpy of liquid water

A Phase diagram of water plotted between temperature and specific entropy illustrate the enthalpy of water at a different state.

Saturated dry steam curve separates super-heated steam from the wet steam region, and saturated liquid curve separates sub-cooled liquid from the wet steam region.

The point where both saturated vapour and saturated liquid curve meets is known as the critical point. At this point water, directly flashed off to vapour.

Note: At critical point, The latent heat of vaporization is equal to zero.

At critical point degree of freedom is zero.

  • Critical point pressure for water is 221.2 bar
  • Critical point temperature of the water is 374℃
  • The line 1-2-3-4-5 represents a constant pressure line.
T S DIA 1
Fig 3: Phase diagram representation on T-S curve

Subcooling: It is the process of decreasing the temperature at constant pressure below the saturated liquid.

Specific enthalpy of liquid water is the difference of enthalpy of water at the saturated liquid line (2) and specific enthalpy of water in sub cool region (1). Unit of specific Enthalpy (h) is kJ/kg.

h1 = h2 – c p(liquid) (T2 – T1)

Where,

h1 = enthalpy of water in sub cool region

h2 or hf = enthalpy of water at saturated liquid curve

Cp (liquid) = 4.18 kJ/kg (specific heat capacity of water)

T2 = Temperature of liquid at saturation point

T1 = Temperature of liquid in sub cool region  

Specific enthalpy of steam

Specific enthalpy of the steam at any arbitrary point (3) in the wet region is given by sum of specific enthalpy at saturation liquid curve at constant pressure and product of dryness fraction and difference of enthalpies at saturation liquid curve and saturation vapour curve as same constant pressure.

h3 = hf + X(hfg)

h3 = specific enthalpy of steam in wet region

hg = specific enthalpy of steam at saturation vapour line

hf = specific enthalpy of steam at saturation liquid line

hfg = hg – hf

Wet Region : It is the mixture of liquid water and water vapour

Dryness Fraction (X): It is defined as the ratio of the mass of water vapour to the total mass of the mixture. The value of dryness fraction is zero for saturated liquid and 1 for saturated vapour.

X = mv/(mv+ml)

Where mv = mass of vapour

        ml = mass of liquid

Specific enthalpy of superheated steam

Super heating: It is a process of increasing the temperature at constant pressure above saturated vapour line.

h5 = h4 + cp(vapour) (T5 – T4)

Where,

h5 = specific enthalpy of steam in super heated state.

h4 = specific enthalpy at saturation vapour curve.

Cp = heat capacity at constant pressure

T4 = Temperature at point 4

T5 = Temperature at point 5

Specific Enthalpy on steam table

Steam table contains thermodynamic data about the properties of water or steam. It is mainly used by the thermal engineers for designing heat exchangers.

Some frequently used values on the steam table has been shown below.

Screenshot 2021 05 10 at 9.29.28 PM
Pressure based saturated steam table (Image credit : www.tlv.com)

Enthalpy and Specific Enthalpy

Enthalpy (H): It represents the total heat content of the system.

The mathematical expression is

H = U + PV

H = Enthalpy of system

U = Internal Energy of system

P = Pressure

V = volume

Change of enthalpy (dH) is defined as the product of mass, specific heat capacity at constant pressure and temperature difference between two state.

dH = mCp(dT)

m = mass of the system

Cp = heat capacity of fluid

dT = change in temperature

SI unit of Enthalpy is kJ

Specific Enthalpy and heat capacity

Specific enthalpy (h) is defined as the summation of specific internal energy and flow work.

The mathematical expression is given by

h = u +Pv

u = specific internal energy

Pv = flow work

SI unit of specific enthalpy kJ/kg

Specific heat capacity (Cp) of water is defined as the amount of heat required to raise the temperature of 1 kg of water by 1 K. For ex specific heat capacity of water is 4184 J/kg-K.

cp = specific heat capacity.

SI unit of specific heat capacity is kJ/kg-K.

Specific enthalpy of combustion

It is defined as the enthalpy change when a substance reacts vigorously with oxygen under standard conditions. It is also known as “heat of combustion”. The enthalpy of combustion of petrol is 47 kJ/g and diesel is 45 kJ/g.

Specific Enthalpy of evaporation

It is defined as the amount of energy that must be added to 1 kg of a liquid substance to transform it completely into gas. The enthalpy of evaporation/vaporization is also known as latent heat of vaporization.

Specific enthalpy of evaporation of steam

The heat energy required by the water at 5 bar pressure to convert it into steam is basically less than the heat needed at atmospheric conditions. With the increase of steam pressure specific enthalpy of evaporation of steam decreases.

Specific Enthalpy of moist air

Specific enthalpy of moist air is given by

h = 1.005*t+ω (2500+1.88 t)

h = enthalpy of moist air kJ/kg

t = Dry Bulb Temperature in ℃

ω = specific humidity or humidity ratio in kg/kg of dry air

Specific Humidity (ω) is defined as the ratio of the mass of water vapour per Kg of dry air in a given volume and given temperature.

Specific enthalpy of saturated steam

The specific enthalpy of a saturated steam at corresponding temperature and pressure is 2256.5 kJ/kg. It is represented by hg.

Specific enthalpy of saturated water

The specific enthalpy of saturated water at standard atmospheric conditions is 419kJ/kg. It is generally represented by hf.

Specific enthalpy of water vapour

At standard atmospheric conditions,i.e 1 bar pressure, water starts boiling at 373.15K. The specific enthalpy (hf)of water vapour at saturated condition is 419 kJ/kg.

Absolute Specific Enthalpy

The enthalpy of the system is measured of total energy in the system. It cannot be measured in absolute value as it depends on change in temperature of the system and can only be measured as the change in enthalpy. For ideal gas, Specific enthalpy is the function of temperature only.

Acrylic Acid Specific Enthalpy

Acrylic acid is used in many industrial products as raw material for Acrylic Easter. It is also used in manufacturing polyacrylates. Specific enthalpy of formation of Acrylic Acid is in the range of -321± 3 kJ/mole.

FAQ/Short Notes

1. Specific Enthalpy of Helium:

Specific heat of helium is 3.193 J/g K. Latent Heat of vapourization of Helium is 0.0845 kJ/mole.

Heat of vaporization of Helium

specific enthalpy
Fig 5: The heat of vapourization of helium (Image credit: people)

2. Can specific enthalpy be negative?

Yes, the enthalpy of formation of ethanol is negative. Enthalpy of formation is defined as the energy removed during the reaction to form compound from elements under standard conditions. The higher negative the enthalpy of formation, the more stable the compounds is formed.

3. Specific enthalpy vs specific heat capacity

Specific enthalpy is the total energy of a unit mass or defined as the sum of specific internal energy and work done across the boundary of the system.

Specific heat capacity is defined as the heat required to raise the temperature of 1 kg of water by 1 K.

4. Specific enthalpy vs specific heat

The heat interaction per unit mass at constant pressure (Isobaric process) is known as specific enthalpy.

5. Air specific enthalpy vs temperature

Specific enthalpy of air is defined as the product of heat capacity of air at constant pressure and change in temperature whereas the temperature is an intensive property of the system by virtue of which heat transfer takes place.

6.Mass enthaply vs specific enthalpy

Mass enthalpy or enthalpy is defined as the total energy content of the system . Its unit is kJ.Specific enthalpy is defined as total energy content of the system per unit mass. Its unit is kJ/kg.

7.Difference between Enthalpy and Entropy

Enthalpy is defined as the total heat content of the system where as the entropy is defined as the total randomness of the system.

8.Why does specific enthalpy of steam on steam tables begin to decrease after about 31 bar?

The liquid and vapour phases of a substance are indistinguishable from each other. If we consider the internal energy of the steam, it should decrease with enthalpy, But as the random vibration of molecules is hindered by other molecules due to increase in pressure.m which results in decrease of specific volume, thereby decreasing internal energy. As the specific enthalpy is defined as the sum of specific internal energy and flow work on boundary of the system, the specific enthalpy also decreases.

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