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 = S niCPmi(T2 - T1) = S 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