Question

Your boss asks you to determine (and quickly) the amount of heat needed to increase the temperature of a gaseous n-octane stream from 25 °C to 800 °C. The stream operates at a flow rate of 125 mol/min with pressure maintained roughly at 1 atm.

a)      Due to the time constraint you assume that the heat capacity is independent of temperature. How much heat do you tell our boss is required?

b)      Later, you decide to calculate the true amount of heat added. What is the actual of amount of heat needed for the temperature change of the n-octane stream?

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Answer 1

(a) Change in temperature T = 800 C - 25 C = 775 C

Heat capacity of n-octane = is 255.7 J.C^-1mol^-1 at 25 C

flow rate = 125 mol/min

Hence the heat required to increase the temperature at constant temperature

= nCT = (125 mol/min) x 255.7 J.K^-1mol^-1 x 775 C = 24771 KJ (answer)

(b) Now if we consider that the value of C changes with temperature, the value of C can be calculated from the following relation.

C = a + bT + c/T²

where a, b and c are constants and have specific value for n-octane.

Q = nCT

Now we can calculate the value of actual Q by integrating the above equation with lower limit of (25+273) K and upper limit of (700+273)K and putting the value of a, b and c for n-octane