### 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 25oC to 700oC?

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 0oC.

therefore, number of gmol of gas in the volume of 15000 litre at 25oC, 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 25oC to 700oC is given by,

H = Σ niCPmi(T2 - T1) = Σ niCPmi (700 - 25)

Where ni is the moles of component 'i', and CPmi 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

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