# PROPERTIES OF STEAM CLASS NOTES FOR MECHANICAL ENGINEERING

**PROPERTIES OF**** STEAM **

**CLASS NOTES FOR**

**MECHANICAL ENGINEERING**

### Specific properties are per kg.

### Examples are specific volume,

### specific values of enthalpy, entropy,

### internal energy and latent heat.

**Symbol**

Small alphabets represent specific properties.

Firstly specific volume =v

Secondly specific enthalpy = h

Thirdly specific entropy = s

Fourthly specific internal energy =u

Specific heat =c_{P}

Reference temperature for the enthalpy and entropy of water is 0^{0}C.

Assumed Enthalpy of water is 0 (ZERO) at 0^{0}C.

Firstly specific heat of ice = 2.1 kJ/kg^{0}C

Secondly specific heat of water = 4.18 kJ/kg^{0}C

Thirdly specific heat of steam vapor = 2.3 kJ/kg^{0}C

Latent heat of ice = 335 kJ/kg

Latent heat of vaporization = 2257 kJ/kg

**Specific enthalpy**

- Therefore, enthalpy of 1 kg of ice at 0
^{0}C becomes negative and is –335kJ/kg. The latent heat of ice is 335 kJ/kg - Enthalpy of water at
^{0}C = 0 kJ/kg - Enthalpy of water say at 11
^{0}C

=m c_{p }dt = 1 x 4.18 x 11=45.98 kJ/kg

4.Enthalpy of water at 100^{0}C

h= 1 x 4.18 x 100 = 418 kJ/kg

5. Enthalpy of water Vapor at 100^{0}C and at

1 atm pressure

= 418 + LH

=418 + 2257 = 2675 kJ/kg

6. Enthalpy of water vapor, say, at 119^{0}C at

1 atm pressure will be

h = 2675 + 1 C_{p vapor} dt

** = 2675 + 1x 2.3x 19**

** = 2675 + 43.7= 2718.7 kJ/kg**

**Dryness Fraction Of Steam**

Symbol of dryness fraction is ‘x’. It is the ratio of mass of vapor to total mass of vapor and liquid.

x = mass of vapor/(mass of vapor +mass of liquid)

Its value will lie between 0 and 1.

- For total liquid, dryness fraction is zero.
- When it is total vapor, dryness fraction is one.
- For some liquid and some vapor. Let its dryness fraction is ‘x’. Value of x is >0 and < 1.
- Enthalpy of wet steam

Wet steam with dryness fraction ‘x’

h_{x} = (1—x)h_{f} +x h_{v}

Where h_{f} is enthalpy of saturated water at its boiling point at a certain pressure

h_{v} is the enthalpy of saturated vapor at its boiling point at a certain pressure

**Specific Volume**

(i) Specific volume of water= volume of 1 kg of water

= 0.001 m^{3}/kg

(ii) Specific volume of wet steam v_{x }=(1—x)v_{f} + x v_{g}

(iii) Find specific volume of super heated steam using Charles law

v_{super }/ T_{super} = v_{sat}/T_{sat}

**Specific Internal Energy**

Internal energy of water of mass m, U = m c_{v }dt

For 1 kg, u = 1 x c_{p} x dt

Say at 10^{0}C, u = 1 x 4.18 x 10 = 41.8 kJ/kg

Internal energy of steam

u = h-p v

**Specific Entropy**

(i) Assume entropy of water as 0 at 0^{0}C.

(ii) Entropy of water say at 10^{0}C

s = c_{p} ln(T/273)= 4.18 ln(283/273) kJ/kg ^{0}C

(iii) Entropy change during phase change = s_{fg} = h_{fg}/T_{sat}

(iv) Entropy of wet steam s_{x} = (1-x) s_{f} + x s_{g}

(v) Entropy of saturated steam s _{sat} = s_{f} + s_{fg} = s_{v}

(vi) Entropy of super heated steam = s_{super}

s _{super}= s _{v} + c _{p vap} ln(T _{super} / T _{sat} )

** SPECIFIC ENTHALPY, ENTROPY AND VOLUME OF SATURATED LIQUID AND VAPOR ARE GIVEN IN STEAM TABLES & CHARTS.**

**STEAM TABLES**

Steam tables and charts give only specific values of steam properties at saturated condition only. Properties given are specific volume, specific enthalpy and entropy for saturated liquid and saturated vapors.

**STEAM CHARTS**

There is another shorter way for analysis of systems. It is by the use of temperature entropy chart and enthalpy entropy chart (also called the Mollier Chart). The steam is the working substance as in steam engines, steam turbines and various space heating applications.

**TEMPERATURE ENTROPY CHART **

Refer to Fig. and concentrate on the following lines which are highly helpful in the analysis.

** **

This chart is extremely helpful in the analysis. Following lines are present on the chart.

1. Outer boundary is a saturated vapor curve. Wet region is below the saturated. Super heated region is above the saturated.

2. Inclined straight lines are constant pressure lines in the wet and super heated regions

3. Vertical lines are constant entropy lines.

4. Horizontal lines are constant temperature lines.

5. Curved lines in the wet region are constant dryness fraction lines.

**Application of properties of steam in Rankine Cycle**

This Cycle uses steam as the working substance. Plot Rankine Cycle on the chart. Read properties from the chart. Use of steam tables consumes more time than charts. Steam tables give properties at some specific pressures and temperatures. Interpolate values at the required temperature and pressure.

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