Rate Processes - Part 1

2 Objectives Know the relationships between rate, flux, and driving force Define the proportionality constants for heat, fluid flow, electricity, and diffusion problems Know how to compute the rate and flux for heat, fluid flow, electricity, diffusion problems Understand 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

6 Example-Water filling a tank The volume in the tank changes at a rate r 1 The water goes past the pipe outlet at flow rate, r 2 For this case, because there is no outlet in the tank, the volume changes at the same rate as the water flows in, thus r 1 = r 2 = r Volume, V Time, t VV tt r r r t

7 Flux - rate per unit cross-sectional area Example: bullets through a target 1 m 2 1 second passes

8 Driving Force - a potential that can result in a flux r A x D in D out Proportionality Constant

9 Fluxes

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

11 Heat Flux Heat Vibrating copper atom Copper rod T in =100 o C T out =0 o C Cross sectional area, A 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: Aluminum Copper Styrofoam

14 Pairs Exercise 2 A 1.00-m long silver rod has a square cross section that is 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 20 o C and -12 o C, respectively. Given that the wall has an area of 120 m 2, how much heat (J/s) is lost through the wall? See Table 12.2 for conductivities

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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

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 (m 3 /s) of glycerin through a 0.01-m diameter, 20-m long pipe with an inlet pressure of 1.5×10 5 Pa and an outlet pressure of 1.3×10 5 Pa.

20 Pairs Exercise 6 Use Excel to complete hotplate.doc