For a high-intensity oxidation process, a stream of pure O_2 (10.0 mol/sec) at 1

Question

For a high-intensity oxidation process, a stream of pure O_2 (10.0 mol/sec) at 100 degree C and 1.0 aim and a stream of pure N_2 (10.0 mol/sec) at 150 degree C and 1.0 atm are combined in a mixer that has a heat loss to the surroundings equal to 209(T - 25) J/sec, where T is the outlet pas mixture temperature in degree C. Calculate the temperature of the exiting gas stream from the mixer. Use the following heat capacity equations: O_2: C_p = 6.15 + 3.1 times 10^3 T N_2: C_p = 6.50 + 1.25 times 10^3 T where T is in K and C_p Is in cal/mol/K Three hundred kilograms per hour of air flow through a well-insulated countereurrent hat exchanger as shown below. Two hundred and thirty kilograms per hour of potassium caronatc (K_2CO_3) aqucous solution are heated by the air.

Explanation / Answer

For this problem you have to be very carefull with the units, this is an application of the energy balance which is

Enthalpy in = Enthalpy out + Change

In this case the change comes from the heat loss caused by the mixer. First let's calculate the enthalpy in

Enthalpy in (assume a basis of 1 sec)

Enthalpy = H = m * Cp * T

For O2

Cp = 6.15 + 3100*T (T = 100 + 273.15), T is temperture in kelvin

Cp = 6.15 + 3100 * (373.15) = 1156771.15 cal / mol K

m = 10 moles

T = 373.15

Apply H = m * Cp * T

H = 10 * 373.15 * 1156771.15 = 4316491546.22 calories

Repeat it for N2

m = 10

T = 423.15 K

Cp = 6.5 + 1250 * (423.15) = 528944

H = m * Cp * T = 10 * 423.15 * 528944 = 2238226536 calories

Total calories entering the mixer (sum) = 6554718082 calories, we must change this value to joules, we do this by multiplying this value by 4.184 so

Total joules entering the mixer = 2.74 x 1010 Joules

We have to do something similar for the values that are going out

Enthalpy out

For O2

H = 4.184 * 10 *  (6.15 + 3100*Tf) * Tf, T in Kelvin

For N2

H = 4.184 * 10 *( 6.5 + 1250 *Tf) * Tf, T in kelvin

Heat loss

H = 209 * (Tf-25) , T in Celsius, change T to kelvin , T Celsius = T kelvin - 273.15

H = 209 * (Tf - 298.15), Tf in kelvin , the result will be already in joules according to the statement

so the global equation is

Enthalpy in = Enthalpy out + Change

2.74 x 1010 Joules = 4.184 * 10 *  (6.15 + 3100*Tf) * Tf + 4.184 * 10 *( 6.5 + 1250 *Tf) * Tf + 209 * (Tf - 298.15)

So the next thing to do is to solve this equation, Im using a spreadsheet to solve this equation, im getting a value of

T = 388.17 Kelvin or 115.02 Celsius

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