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Chapter 2 Heat Effects
Chemical Engineering Thermodynamics
2.1 Sensible Heat2.2 Latent Heat of Pure Substances
Chapter Outline
Design of reactors requires knowledgeof the heat rate which depends on the heat effects associated with the chemical reactions.
Thermodynamics is applied to evaluate most of heat effects that accompany physical and chemical reactions.
2.1 Sensible HeatThe molar or specific internal energy, U of a substances may be expressed as a function of 2 state variables.As the variables randomly selected as temperature., T and molar or specific volume, V;
dV VUdT
TUdU
TV
VV T
UC
constant-= volume heat capacity
dV VUdTCdU
TV
dV VUdTCdU
TV
0 For any constant-volume process, regardless of substance.
Internal energy independent of volume. True for ideal gases and incompressible fluids.
dTCdU V 2
1
T
TV dTCU
For mechanically reversible constant-volume process, UQ
2
1
T
TV dTCUQ
Integrate
The molar or specific enthalpy, H of a substances may be expressed as afunction of temperature, T and pressure, P;
dP PHdT
THdH
TP
PP T
HC
constant-= pressure heat capacity
dP PHdTCdH
TP
dP PHdTCdH
TP
0 For any constant-pressure process, regardless of substance.
Enthalpy independent of volume. True for ideal gases and approximately true for low-pressure gases
dTCdH P 2
1
T
TPdTCH
Integrate
For mechanically reversible constant-pressure, closed-system process, HQ
2
1
T
TPdTCHQ
Temperature Dependence of the Heat Capacity
2
1
T
TV dTCUQ
2
1
T
TPdTCHQ
To integrate and
required knowledge of
the temperature dependence of the heat capacity.
Which one stays hot longer after being removed from heat source?
The substance with the higher specific heat capacity stays hot
longer.
The idea of heat capacity…
Heat capacity is given by 2 simplest expressions;
2 TT αR
CP 2 cT bTaR
CPand
Where , , , a, b and c are constants characteristic of the particular substance.
They are combined to give:
22 DTCT BTAR
CP
Idea-gas-state heat capacities, andare dependence on temperature but independent of pressure.
igPC ig
VC
22 DTCT BTAR
C igP
Temperature-dependence heat capacityis expressed by:
Value of parameter are given in Table C.1 (pg. 684) for common organic and inorganic gases.
Two ideal-gas heat capacities are related:
1R
CR
C igP
igV
Table C.1
Try this…
Given the molar heat capacity of methane in the ideal-gas-state as functions of temperature
263 10164.210081.9702.1 TTR
C igP
Calculate the value of heat capacity at 87°C.
Evaluation of the Sensible Heat Integral
Now, we can calculate or at given and by integrating .
Q H 0TT
PC
dTCP is solved as a function of followed by integration
T
113
12
1
0
330
2200
0
TDTC
TBATdTCT
T P
0TT
0
20
220
00
13
12
0
TT
TDTC
TBATdTC
T
T P
If or were given and asked to calculate the equation is rearranged:
Q HT
The quantity in square bracket is identify as where is mean heat capacity.
RC
HP HPC
Hence, can be calculated using mean heat capacity,
HHPC
0TTHCH P
0TC
HTHP
Solution for if is given, T HPC
Try this…
By using Table C.1, calculate the heat required to raise the temperature of 1 mol methane from 260 to 600°C in a steady-flowprocess. Methane is considered in ideal-gasstate.
2.2 Latent Heat of Pure SubstancesWhen a pure substance if liquefied from solid state orvaporized from liquid at constant pressure, no changein temperature occurs.
However, the process requires the transfer of finite amount of heat to the substance. These heat effects are called latent heat of fusion and latent heat of vaporization.
Example: Water
There are coexistance of two phases.
Latent heat accompanying a phase change is a function of temperature and related to Clapeyron equation:
dTdPVTH
sat
H = latent heatV
For pure substance at ,T
= volume change accompanying the phase change
satP = saturation pressure
In the vaporization of a pure liquid: = the slope of the vapor pressure-vs-temperature curve at the temperature of interest.
dTdP sat
V = the difference between molar volumeof saturated vapor and saturated liquid.
H = latent heat of vaporization
H can be calculated from vapor-pressure and volumetric data.
Rough estimates of heat of vaporization forpure liquids at their normal boling points are given by Trounton’s rule;
10
n
n
RTH
where is the absolute temperature of the boiling point.
nT
Ar: 8.0; N2:8.7; O2:9.1; HCl:10.4; C6H6:10.5;H2S:10.6; H2O: 13.2
Estimation of heat of vaporization at normal boiling point proposed by Riedel:
nr
c
n
n
TP
RTH
930.0013.1ln092.1
where is the critical pressure (bar), is the reduced temperature at .
cPnr
T nT
Estimation of heat of vaporization at any temperature from the known value at singletemperature value proposed by Watson:
38.0
1
2
1
2
11
r
r
TT
HH
Try this…
Given the latent heat of vaporization of water at 100°C is 2,257 Jg-1, estimate the latent heat at 300°C.
What have you learned…