# Specific properties of water and steam

**Specific properties of water and steam**

**Definition**

Specific properties are per kg. Examples are specific volume, specific enthalpy, specific entropy, specific internal energy and specific latent heat.

**Symbol**

These specific properties are represented by the small alphabet like v, h,s,u,c_{P} etc.

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

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

Specific heat of ice = 2.1 kJ/kg^{0}C, Specific heat of water = 4.18 kJ/kg^{0}C and Specific heat of steam vapor = 2.3 kJ/kg^{0}C

Latent heat of ice = 335 kJ/kg and Latent heat of vaporization = 2257 kJ/kg

**Specific enthalpy**

- Therefore, enthalpy of 1 kg of ice at 0
^{0}C will become negative and will be –335kJ/kg. as 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

=mc_{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**

It is represented by ‘x’. In a certain sample of steam and water, it is the ratio of mass of vapor to the mass of vapor and mass of liquid.

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

Its value will lie between 0 and 1.

- When it is total liquid, dryness fraction is zero.
- When it is total vapor, dryness fraction is one.
- 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) Specifc volume of super heated steam is found by using Charles law

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

**SPECIFIC INTERNAL ENERGY **

Internal energy of water of mass m, U = mc_{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-pv

**SPECIFIC ENTROPY**

(i) Entropy of water at 0^{0}C is taken as zero.

(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 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} )

**NOTE: ONLY SATURATED VALUES OF ENTHALPY, ENTROPY AND VOLUME OF LIQUID AND VAPOR ARE AVAILABLE FROM THE STEAM TABLES AS WELL AS FROM CHARTS.**