Lecture_27a_for_web - Section 8.3 in F&R Sensible heat:...

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Section 8.3 in F&R – Sensible heat: net change in heat causes a change in temperature V V T U C = ˆ T C dT T C U V T T V Δ = = Δ 2 1 ) ( ˆ C V is not constant over T range C V constant over T range In a process where a single phase substance gets heated or cooled, the temperature changes. The temperature change depends on the substances ability to hold heat, or it’s heat capacity . For constant volume processes, we have defined heat capacity at constant volume as: [T 3 T 4 ] [T 1 T 2 ] Û (J/kg) T ( o C) T 1 T 2 T 3 T 4 V is constant
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P P T H C = ˆ T C dT T C H P T T P Δ = = Δ 2 1 ) ( ˆ C P is not constant over T range C P constant over T range For constant pressure processes, we have defined heat capacity at constant pressure as: Some simplifying assumptions: Pure substances • Liquids & solids: C P ~ C V • Ideal gases: C P = C V +R • Kopp’s Rule • Chueh-Swanson method • Otherwise: use table or correlation Mixtures • Take weighted average of component’s heat capacities • For dilute mixtures, neglect the contribution of the solute • Ideal gases: C P = C V +R 3 2 dT cT bT a C P + + + = ( ) = components all i ) ( y ) ( T C T C i P mix P Valid only when enthalpy of mixing can be neglected!
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Energy balance on a gas preheater A stream containing 10% CH 4 and 90% air by volume is to be heated from20 o C to 300 o C. Calculate the required rate of heat input in kW if the flow rate of the gas is 2.00 x 10 3 L (STP)/min. heater 2000 L(STP)/min, 20 o C n mol/min 0.100 mol CH 4 /mol 0.900 mol air/mol Q kW 300 o C n mol/min 0.100 mol CH 4 /mol 0.900 mol air/mol min 3 . 89 ) ( 4 . 22 1 min ) ( 2000 mol STP L mol STP L n = = & min 93 . 8 min 3 . 89 100 . 0 4 4 molCH mol mol molCH n methane = = & min 4 . 80 min 3 . 89 900 . 0 molAir mol mol molAir n air = = &
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Energy balance on a gas preheater A stream containing 10% CH 4 and 90% air by volume is to be heated from20 o C to 300 o C. Calculate the required rate of heat input in kW if the flow rate of the gas is 2.00 x 10 3 L (STP)/min. heater 2000 L(STP)/min, 20 o C n mol/min 0.100 mol CH 4 /mol 0.900 mol air/mol Q kW 300 o C n mol/min 0.100 mol CH 4 /mol 0.900 mol air/mol min 3 . 89 ) ( 4 . 22 1 min ) ( 2000 mol STP L mol STP L n = = & min 93 . 8 min 3 . 89 100 . 0 4 4 molCH mol mol molCH n methane = = & min 4 . 80 min 3 . 89 900 . 0 molAir mol mol molAir n air = = &
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H Q & & Δ = ∑∑ = out in i i i i H n H n Q ˆ ˆ & & heater 2000 L(STP)/min, 20 o C n mol/min 0.100 mol CH 4 /mol 0.900 mol air/mol Q kW 300 o C n mol/min 0.100 mol CH 4 /mol 0.900 mol air/mol Substance n in Ĥ in n out Ĥ out (mol/min) (kJ/mol) (mol/min) (kJ/mol) CH 4 8.93 0 8.93 Ĥ 1 Air 80.4 Ĥ 2 80.4 Ĥ 3 Reference states: CH 4 (g, 20 o C, 1 atm), Air (g, 25 o C, 1 atm) + + = = C C C C CH P dT T x T x T x dT C H 300 20 3 12 2 8 3 300 20 , 1 ) 10 0 . 11 10 3661 . 0 10 469 . 5 03431 . 0 ( ˆ 4 Ĥ 1 = 12.09 kJ/mol
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Substance n in Ĥ in n out Ĥ out (mol/min) (kJ/mol) (mol/min) (kJ/mol) CH 4 8.93 0 8.93 12.09 Air 80.4 Ĥ 2 80.4 Ĥ 3 Reference states: CH 4 (g, 20 o C, 1 atm), Air (g, 25
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Lecture_27a_for_web - Section 8.3 in F&R Sensible heat:...

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