Solved Problem On Energy Requirement for Heating

                                       

                             


 Energy Requirement for Heating

The analysis of 15000 litre of gas mixture at standard conditions is as follows:

CO₂ = 9.5% ; SO₂ = 0.5% ; O₂ = 12.0% ; N₂ = 78.0%.

How much heat must be added to this gas to change its temperature from 25^oC to 700^oC?

Data: Specific heat values in kcal/(kmol.^oK)

Gas  CO2 SO2 O2 N2
Cp at 25oC 8.884 9.54 7.017 6.961
Cp at 700oC 11.303 11.66 7.706 7.298

Calculations:

Basis: 15000 litre of gas

22.4 litre is occupied by 1 gmol of gas at at 0^oC.

therefore, number of gmol of gas in the volume of 15000 litre at 25^oC, is estimated as:

PV = nRT (Ideal gas equation)

From the above equation,

n₂P₁V₁/T₁ = n₁P₂V₂/T₂

here P₁ and P₂ are the same.

Therefore,

n₂ x 22.4 / 273 = 1 x 15000 / (273 + 25)

n₂ = 613.5 gmol = 0.6135 kmol

Component	Mole fraction	No of moles, kmol
CO2	0.095	0.6135 x 0.095 = 0.0583
SO2	0.005	0.6135 x 0.005 = 0.0031
O2	0.12	0.6135 x 0.12 = 0.0736
N2	0.78	0.6135 x 0.78 = 0.4785

Heat required (H) to raise the temperature from 25^oC to 700^oC is given by,

H = S n_iC_Pmi(T₂ - T₁) = S n_iC_Pmi (700 - 25)

Where n_i is the moles of component 'i', and C_Pmi is the mean molal specific heat of component 'i'.

The calculations are shown in the following table.

Component	kmol	CP at 25oC kcal/(kmol.oK)	CP at 700oC kcal/(kmol.oK)	CPm kcal/(kmol.oK)	Heat to be added, kcal
CO2	0.0583	8.884	11.303	(8.884 + 11.303)/2 = 10.0935	0.0583 x 10.0935 x (700 - 25) = 397.2
SO2	0.0031	9.54	11.66	10.6	22.18
O2	0.0736	7.017	7.706	7.3615	365.72
N2	0.4785	6.961	7.298	7.1295	2302.74
Total heat to be added					3087.84 kcal