changes in temperature

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CHANGES IN TEMPERATURE

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Page 1: Changes in Temperature

CHANGES IN TEMPERATURE

Page 2: 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

Page 3: Changes in Temperature

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.

Page 4: Changes in Temperature

Devided into two categories:

Heat capacity at constant volume denoted by Cv

Heat capacity at constant pressure denoted by Cp

HEAT CAPACITIES

Page 5: Changes in Temperature

Heat capacity at constant volume, Cv

Page 6: Changes in Temperature

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

Page 7: Changes in Temperature

Heat capacity at constant pressure, Cp

Page 8: Changes in Temperature

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

Page 9: Changes in Temperature

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

Page 10: Changes in Temperature

Simple relationship between Cp≈Cv in two cases:

Liquids and solids: Cp≈CvIdeal gases: Cp=Cv + R

Where: R=gas constant

Page 11: Changes in Temperature

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

Page 12: Changes in Temperature

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

Page 13: Changes in Temperature

(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

Page 14: Changes in Temperature

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

Page 15: Changes in Temperature

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

Page 16: Changes in Temperature

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