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…