ABP (aprendizaje basado en problemas)

(1) Evaluation the Enthalpy of Steam Let

h_f = Heat of the liquid or sensible heat of water in KJ/kg h_fg = Latent heat of vapourisation of steam in KJ/kg

t_s = Saturation temperature in 0ºC corresponding to the given pressure.

t_sup = Temperature of superheated steam in ºC x = dryness fraction of wet saturated steam

C_p = Sp. Heat of superheated steam at constant pressure in KJ/kg.k.

Temp.InC

hr

tsºC

O

xhtghtg

H_sup H_dry H_wes

tsºC tsºC

Fig 5.6 (a) Enthalpy of dry saturated steam

1 kg of water will be first raised to saturation temperature (t_s) for which h_f (sensible heat of water) quantity of heat will be required. Then 1 kg of water at saturation temperature will be transformed into 1 kg of dry saturated steam for which h_fg (latent heat of steam) will be required. Hence enthalpy of dry saturated steam is given by

H_dry (or h_g) = h_f + h_fg kJ/kg (b) Enthalpy of wet saturated steam

1 kg of water will be first raised to saturation temperature (t_s) for which h_f (sensible heat of water) will be required. Then ‘x’ kg of water at saturation temperature will be transformed into ‘x’ kg of dry saturated steam at the same temperature for which x.h_fg amount of heat will be required. Hence enthalpy of wet saturated steam is given by

H_wet= h_f + x.h_fgkJ/kg (c) Enthalpy of superheated steam

1 kg of water will be first raised to saturation temperature (t_s) for which h_f (sensible heat of water) will be required. Then, 1kg of water at saturation temperature will be transformed into 1kg dry saturated steam at the same temperature for which h_fg (latent heat of steam) will be required. Finally, 1kg dry saturated steam will be transformed into 1kg superheated steam at the same pressure for which heat required is

1 × C_p(t_sup –t_s) = Cp (t_sup – t_s) kJ

Hence enthalpy of superheated steam is given by H_sup= h_f + h_fg + C_p (t_sup – t_s) kJ/kg

(2) Evaluation of heat Required

Heat required to generate steam is different from ‘total heat’ or enthalpy of steam. Heat required to generate steam means heat required to produce steam from water whose initial temperature is tºC (say) which is always greater than 0ºC. Total heat or enthalpy of steam means heat required to generate steam from water whose initial temperature is 0°C. If, however, initial temperature of water is actually 0°C, then of course heat required to generate steam becomes equal to total heat or enthalpy of steam.

hr

tsºC

Heat in KJ/kg tsºC

O

htg

Q_sup Q_dry Q_wet h¢

xhtg tsºC

Fig 5.7 (a) When steam is dry saturated

heat required to generate steam is given by Q_Dry=h_f + h_fg - h’ kJ/kg,

where h’ = heat required to raise 1 kg water from 0°C to the given initial temperature (say t°C) of water

= mst =1 × 4.2 × (t – 0) = 4.2t kJ [sp. heat of water = 4.2 kJ/kg K].

(b) When steam is wet saturated, heat required to generate steam is given by Q_wet = h_f + x.h_fg -h’ kJ/kg.

(c) When steam is superheated, heat required is given by Q_sup =h_f + h_fg + C_P(t_sup - t_s) - h’ kJ/kg.

(3) Evaluation of Specific Volume of Steam

Specific volume of steam means volume occupied by unit mass of steam. It is expressed in m³ /kg. Specific volume of steam is different at different pressure. Again, corresponding to a given pressure specific volume of dry saturated steam, wet saturated steam and superheated steam will be different from one another.

(a) Sp. volume of dry saturated steam (V_g or V_Dry)

It is the volume occupied by unit mass of dry saturated steam corresponding to the given pressure of steam generation.

Sp. volume of dry saturated steam corresponding to a given pressure can be found out by experiment.

However, sp. volume of dry saturated steam corresponding to any pressure of steam generation can be found out directly from steam table. In the steam table, ‘v_g’ denotes the sp. volume of dry saturated steam in “m³/kg”,

(b) Specific volume of wet saturated steam (V_wet)

It is the volume occupied by unit mass of wet saturated steam corresponding to the given pressure of steam generation.

Sp. volume of wet saturated steam is given by

V_wet = volume occupied by ‘x’ kg dry saturated steam + volume occupied by (1 – x) kg. water, where,

x = dryness fraction of wet saturated steam.

Let v_g = sp. volume of dry saturated steam in m³/kg corresponding to given pressure of wet saturated steam.

v_f = sp. volume of water in m³/kg corresponding to the given pressure of wet saturated steam.

Then,

V_wet = x.vg + (1 – x) v_f m³/kg.

Since (1 – x) v_f is very small compared to x.v_g , it is neglected.

[Average value of v_f = 0.001 m³/kg upto atmospheric pressure].

So,

V_wet = xv_g m³/kg.

(c) Specific volume of superheated steam

It is the volume occupied by unit mass of superheated steam corresponding to the given pressure of superheated steam generation. Superheated steam behaves like a perfect gas. Hence the law

1 1 2 2

1 2

PV = P V

T T

is applicable to superheated steam. Let

v_g = sp. volume of dry saturated steam corresponding to given pressure of steam generation is m³ /kg.

T_S = absolute saturation temperature corresponding to the given pressure of steam generation.

T_sup = absolute temperature of superheated steam P = pressure of steam generation

V_sup = required specific volume of superheated steam.

Then, in the above formula, P₁ = P₂

(4) Evaluation of Internal Energy of Steam

It is the actual heat energy stored in steam above the freezing point of water.

We know that enthalpy = internal energy + pressure energy

= U + PV, where

U = internal energy of the fluid PV = pressure energy of the fluid P = pressure of the fluid V = volume of the fluid.

If ‘U’ is in kJ/kg, ‘P’ is in kN/m² and ‘V’ is in m³/kg,

then U + PV denotes specific enthalpy is kJ/kg. [sp. enthalpy means enthalpy per unit mass]

From the above equation, we get u = enthalpy – PV = H – PV kJ/kg,

where H = enthalpy per unit steam in kJ/kg.

(a) Internal energy of dry saturated steam is given by U_Dry = H_Dry – P.v_g kJ / kg,

where H_Dry (or h_g) = enthalpy of dry saturated steam in kJ/kg.

v_g = sp. volume of dry saturated steam in m³/kg, and P = pressure of steam generation in kN/m²

(b) Internal energy of wet saturated steam is given by u_wet = H_wet - P.V_wet kJ/kg,

where

H_wet = enthalpy of wet saturated steam in kJ/kg V_wet = sp. volume of wet saturated steam in m³/kg (c) Internal energy of superheated steam is given by

u_sup = H_sup - P.v_sup kJ^/ kg, where

H_sup = enthalpy of superheated steam in kJ/kg.

v_sup = sp. volume of superheated steam in m³/kg.