Rate Processes - Part 1

2

Objectives

Know the relationships between rate, flux, and driving forceDefine the proportionality constants for heat, fluid flow, electricity, and diffusion problemsKnow how to compute the rate and flux for heat, fluid flow, electricity, diffusion problemsUnderstand the concept of resistance

3

RAT 12

4

Terminology

Thermodynamics told us where a process was going

For example, if you put a pot of water over a big enough flame, it will boil…eventually

Rate processes tells us how long it takes to get there

5

Rate

Rate is the amount a quantity changes per unit time

Flow rate is the amount of quantity N that flows by a point in a given length of time

t

N

t

Nr

in time Change

Quantity in Change Rate

t

Nr Rate Flow

6

Example-Water filling a tank

The volume in the tank changes at a rate r1

The water goes past the pipe outlet at flow rate, r2

For this case, because there is no outlet in the tank, the volume changes at the same rate as the water flows in, thus r1 = r2 = r

Vol

ume,

V

Time, t

V

t

rr r

t

7

Flux - rate per unit cross-sectional area

area sectional-cross

rate Flux

A

rJ

area) sectional-ss(time)(cro

amount

At

N

Example: bullets through a target

1 m2

1 second passes 2m· second

bullets 5J

8

Driving Force - a potential that can result in a flux

r

A

xDin Dout

x

DDK

x

DK

x

D

A

rJ outin

Proportionality Constant

9

Fluxes

Quantity, N Driving Force, D

Heat Temperature

Fluids Pressure

Electric Current Voltage

Chemical Species Concentration

10

Heat Flux

Heat, Q, energy flows as a result of a temperature differenceHeat flux, Jheat, is the amount of heat (energy) that flows past a cross sectional area, A, in a given time, t

At

QJheat

Heat

11

Heat Flux

HeatVibrating copper atom

Copper rod

Tin=100oC Tout=0oCCross sectionalarea, A

x

Tk

x

TTk

At

QJ outin

heat

Thermal conductivity

Heat

12

Thermal Conductivity

The proportionality constant for heat flux is called the thermal conductivity.

If material has a high thermal conductivity, then the heat flux (flow rate per unit area) is high, so the heat flows ‘easily’ for a given T. This material is called a conductor.For a material with the same T, if k is small, the heat flux is smaller, thus the flow is more difficult. This material is called an insulator.

13

Pair Exercise 1

For the SI system, what are the units of k?Based on your personal experience, classify the following as conductors or insulators:

AluminumCopperStyrofoam

14

Pairs Exercise 2

A 1.00-m long silver rod has a square cross section that is 0.200 m on a side. One end is immersed in boiling water and the other end is immersed in an ice bath. How much heat (J/s) flows down the rod?

15

Pairs Exercise 3

A house has brick walls 8.00 cm thick. On a winter day, the temperatures on the inner and outer surfaces of the wall were 20oC and -12oC, respectively. Given that the wall has an area of 120 m2, how much heat (J/s) is lost through the wall?

See Table 12.2 for conductivities

1614

Fluid Flux

• I n the figure above, the volume of fluid, V,flows as a result of a pressure diff erence.

• Fluid flux, J fl uid, is the volume that flows pasta cross sectional area, A, in a given time, t

V A

xPin Pout

d

17

Fluid Flux

Fluid flux is given by the Poiseuille equation:

Where is the viscosity (sort of like thickness, or flow resistance)This equation is valid only for laminar (nonturbulent) flow. The flow is laminar provided

x

PA

x

PPA

tA

VJ outin

fluid

88

2300fluidJd

18

Pair Exercise 4

For the SI system, what are the units of ?Which is more viscous, water or molasses?Do gases have viscosity?

19

Pairs Exercise 5

Calculate the flowrate (m3/s) of glycerin through a 0.01-m diameter, 20-m long pipe with an inlet pressure of 1.5×105 Pa and an outlet pressure of 1.3×105 Pa.

20

Pairs Exercise 6

Use Excel to complete hotplate.doc