Question

In a power station, the saturated steam is generated at 200ºC by transferring the heat from hot gases in a steam boiler. Find the increase in total entropy of the combined system of gas and water and increase in unavailable energy due to irreversible heat transfer. The gases are cooled from 1000°C to 500°C and all the heat from gases goes to water. Assume water enters the boiler at saturated condition and leaves as saturated steam. 

Take : c_pg (for gas) = 1.0 kJ/kg K, h_fg (latent heat of steam at 200°C) = 1940.7 kJ/kg. Atmospheric temperature = 20°C. 

Obtain the results on the basis of 1 kg of water.

Answer 1

Temperature of saturation steam = 200 + 273 = 473 K 

Initial temperature of gases = 1000 + 273 = 1273 K 

Final temperature of gases = 500 + 273 = 773 K 

For gases : c_pg = 1 kJ/kg K 

Latent heat of steam of 200°C 

saturation temperature, h_fg = 1940.7 kJ/kg 

Atmospheric temperature = 20 + 273 = 293 K 

Heat lost by gases = Heat gained by 1 kg saturated water when it is converted to steam at 200°C.

m_gc_pg (1273 – 773) = 1940.7

[where m_g = mass of gases, c_pg = specific heat of gas at constant pressure]

m_g = \(\cfrac{1940.7}{(1273-773)}\) = 3.88 kg

Change of entropy of m_g kg of gas,

Change of entropy of water (per kg) when it is converted into steam,

Net change in entropy due to heat transfer 

= – 1.935 + 4.103 = 2.168 kJ/K.

Increase in unavailable energy due to heat transfer 

= 293 × 2.168, i.e., cross hatched area 

= 635.22 kJ per kg of steam formed.