M.Sc.-II(Physics)�Thermal Properties

ISSUES TO ADDRESS...

• How do materials respond to the application of heat?

• How do we define and measure...

-- heat capacity?

-- thermal expansion?

-- thermal conductivity?

-- thermal shock resistance?

• How do the thermal properties of ceramics, metals, � and polymers differ?

Chapter 19 -

Heat Capacity

2

• Quantitatively: The energy required to produce a unit rise in � temperature for one mole of a material.

heat capacity

(J/mol-K)

energy input (J/mol)

temperature change (K)

The ability of a material to absorb heat

Chapter 19 -

Dependence of Heat Capacity on Temperature

3

• Heat capacity...

-- increases with temperature

-- for solids it reaches a limiting value of 3R

• From atomic perspective:

-- Energy is stored as atomic vibrations.

-- As temperature increases, the average energy of � atomic vibrations increases.

Adapted from Fig. 19.2, Callister & Rethwisch 8e.

R = gas constant

3R

= 8.31 J/mol-K

C_v = constant

Debye temperature

(usually less than T

room

)

T (K)

θ

D

0

0

C_v

Chapter 19 -

Atomic Vibrations

Atomic vibrations are in the form of lattice waves or phonons

4

Adapted from Fig. 19.1, Callister & Rethwisch 8e.

Chapter 19 -

Specific Heat: Comparison

5

increasing c_p

• Why is c_p significantly

larger for polymers?

C_p (heat capacity): (J/mol-K)

Chapter 19 -

Thermal Expansion

6

Materials change size when temperature � is changed

T_initial

T_final

 _initial

 _final

T_final > T_initial

Chapter 19 -

Atomic Perspective: Thermal Expansion

7

Adapted from Fig. 19.3, Callister & Rethwisch 8e.

Asymmetric curve:

-- increase temperature, � -- increase in interatomic � separation � -- thermal expansion

Chapter 19 -

Coefficient of Thermal Expansion: Comparison

8

• Q: Why does α_

generally decrease

with increasing

bond energy?

Selected values from Table 19.1, Callister & Rethwisch 8e.

Polymers have larger α_ values because of weak secondary bonds

Chapter 19 -

Thermal Expansion: Example

Ex: A copper wire 15 m long is cooled from �40 to -9ºC. How much change in length will it experience?

9

Chapter 19 -

Thermal Conductivity

10

The ability of a material to transport heat.

temperature

gradient

thermal conductivity (J/m-K-s)

heat flux

(J/m²-s)

• Atomic perspective: Atomic vibrations and free electrons in � hotter regions transport energy to cooler regions.

T₂

T₂ > T₁

T₁

x₁

x₂

heat flux

Fourier’s Law

Chapter 19 -

Thermal Conductivity: Comparison

11

• Metals

atomic vibrations and motion of free electrons

k (W/m-K)

Energy Transfer�Mechanism

Material

Selected values from Table 19.1, Callister & Rethwisch 8e.

Chapter 19 -

Thermal Stresses

12

• Occur due to:

-- restrained thermal expansion/contraction

-- temperature gradients that lead to differential � dimensional changes

Thermal stress

= σ

Chapter 19 -

Example Problem

13

-- A brass rod is stress-free at room temperature (20ºC).

-- It is heated up, but prevented from lengthening.

-- At what temperature does the stress reach -172 MPa?

T₀

 ₀

Solution:

Original conditions

Chapter 19 -

Example Problem (cont.)

14

The thermal stress can be directly calculated as

Chapter 19 -

Thermal Shock Resistance

15

• Occurs due to: nonuniform heating/cooling

• Ex: Assume top thin layer is rapidly cooled from T₁ to T₂

Tension develops at surface

Chapter 19 -

Thermal Protection System

16

• Application:

Space Shuttle Orbiter

• Silica tiles (400-1260ºC):

-- large scale application

-- microstructure:

Fig. 19.2W, Callister 6e. (Fig. 19.2W adapted from L.J. Korb, C.A. Morant, R.M. Calland, and C.S. Thatcher, "The Shuttle Orbiter Thermal Protection System", Ceramic Bulletin, No. 11, Nov. 1981, p. 1189.)

Fig. 19.3W, Callister 5e. (Fig. 19.3W courtesy the National Aeronautics and Space Administration.)

Fig. 19.4W, Callister 5e. (Fig. 219.4W courtesy Lockheed Aerospace Ceramics

Systems, Sunnyvale, CA.)

~90% porosity!

Si fibers

bonded to one

another during

heat treatment.

100 μm

Chapter-opening photograph, Chapter 23, Callister 5e (courtesy of the National Aeronautics and Space Administration.)

Chapter 19 -

17

THERMAL DIFFUSIVITY

It measures the ability of a material to conduct thermal energy relative to its ability to store thermal energy.It has the SI unit of m²/s. Thermal diffusivity is usually denoted by α

The formula is:

​

α = k/(c x rho )

where

k is thermal conductivity (W/(m·K))

rho is density (kg/m³)

c is specific heat capacity (J/(kg·K))

Chapter 19 -

Summary

18

The thermal properties of materials include:

• Heat capacity:

-- energy required to increase a mole of material by a unit T

-- energy is stored as atomic vibrations

• Coefficient of thermal expansion:

-- the size of a material changes with a change in temperature

-- polymers have the largest values

• Thermal conductivity:

-- the ability of a material to transport heat

-- metals have the largest values

• Thermal shock resistance:

-- the ability of a material to be rapidly cooled and not fracture

� -- is proportional to

Chapter 19 -

ANNOUNCEMENTS

19

Core Problems:

Self-help Problems:

Reading:

Chapter 19 -