changes in temperature
TRANSCRIPT
CHANGES IN TEMPERATURE
Heat that must be transfer to raise or lower the temperature of a substances.
Quantity of heat required to produced temperature can be determine from first law of thermodynamics.
. . Q = ∆U (Closed System) . . Q = ∆H (Open System)
SENSIBLE HEAT
To determine the sensible heat requirement for a heating or cooling process, ability in determining ∆U or ∆H for specified temperature change is necessary.
Specific internal energy of a substances depend strongly on temperature.
Devided into two categories:
Heat capacity at constant volume denoted by Cv
Heat capacity at constant pressure denoted by Cp
HEAT CAPACITIES
Heat capacity at constant volume, Cv
0
2
1
2
1
( ) lim
( )
( )
( )
T
T
T
TP
T
U UCv T p
T T
dU Cv T dT
U Cv T dT
U C T dT
Heat capacity at constant pressure, Cp
0
2
1
2
1
( ) lim
( )
( )
( )
PT
P
TP
T
TP
T
H HC T p
T T
dH C T dT
H C T dT
H V P C T dT
Expressed in any unit of energy per unit amount per unit temperature interval
Example: J/(mol.K) or Btu/(lbm.°F) Function of temperature and are expressed
in polynomial form:
Cp = a + bT + cT2 + dT3
HEAT CAPACITY FORMULAS
Simple relationship between Cp≈Cv in two cases:
Liquids and solids: Cp≈CvIdeal gases: Cp=Cv + R
Where: R=gas constant
Polynomial expression for Cp:
◦Refer Table B.2◦Usually based on experimental data for
listed compounds◦Provide a basis for accurate calculations
of enthalpy changes
ESTIMATION OF HEAT CAPACITIES
Kopp’s rule:◦A simple empirical method for estimating
the heat capacity of a solid or liquid at or near 20ºC
◦Cp for a molecular compound is the sum of contributions (given in Table B.10) for each element in the compound
(Cp)ca(OH)2 =(Cpa)ca + 2(Cpa)o+2(Cpa)H = [26+(2 X 17) +(2X 9.6)]J/(molºC) = 79 J/(mol.ºC)
Example
1.The heat capacity at constant pressure of hydrogen cyanide is given by the expression
QUESTION
/( . ) 35.3 0.0291 ( )pC J mol c T c
a) Write an expression for heat capacity at constant volume for HCN, assuming ideal gas behavior
b)Calculate ∆H(J/mol) for the constant pressure process
( , 25 ,0.80 ) ( ,100 ,0.80 )HCN V C atm HCN V C atm
c) Calculate ∆U( J/mol) for the constant volume process
( , 25 ,50 3/ ) ( ,100 ,50 3/ )HCN V C m kmol HCN V C m kmol