Thermal Properties

Materials Science · FE Reference Handbook section

Materials Science

3 formulas

10 exam-style examples

~51 min

All Materials Science lectures

Handbook notes for this section

Definitions and conditions exactly as the handbook states them.

The thermal expansion coefficient is the ratio of engineering strain to the change in temperature.
Specific heat (also called heat capacity) is the amount of heat required to raise the temperature of something or an amount of
At constant pressure the amount of heat (Q) required to increase the temperature of something by ∆T is Cp∆T, where Cp is the
At constant volume the amount of heat (Q) required to increase the temperature of something by ∆T is Cv∆T, where Cv is the
An object can have a heat capacity that would be expressed as energy/degree.
The heat capacity of a material can be reported as energy/degree per unit mass or per unit volume.

Core formulas for this FE topic

Definitions, applicability, units, assumptions and worked examples for each relation.

Worked exam-style examples

The four ways this section is written on the real exam — thoughts first, then equations, then substitution.

Example 1

Steady heat flow through a wall — Thermal Properties

A 1.0 ft thick concrete wall of area 390 ft² has k = 1.7 Btu/(hr·ft·°F) and a 65°F temperature difference. What is the heat flow rate?

Given

k = 1.7 Btu/hr·ft·°F
$A = 390 ft^{2}$
ΔT = 65°F
$t = 1.0 ft$

Find

Heat flow q

Start with the thinking

Fourier's law for a plane wall is linear in ΔT.
Thickness divides, area multiplies.

Step-by-step solution

Fourier — q = kAΔT/t
Substituting
$q = 1.7(390)(65)/1.0$
Evaluate
$q = 43,095 Btu/hr$

Answer:

q ≈ 43,095 Btu/hr

Why the other options are there

43,095 Btu/hr (thickness multiplied)
110.5 Btu/hr (area omitted)

Reference: FE Reference Handbook — Materials Science → Thermal Properties

Example 2

Steady heat flow through a wall — Thermal Properties (2)

A 1.1 ft thick concrete wall of area 188 ft² has k = 0.8 Btu/(hr·ft·°F) and a 47°F temperature difference. What is the heat flow rate?

Given

k = 0.8 Btu/hr·ft·°F
$A = 188 ft^{2}$
ΔT = 47°F
$t = 1.1 ft$

Find

Heat flow q

Start with the thinking

Fourier's law for a plane wall is linear in ΔT.
Thickness divides, area multiplies.

Step-by-step solution

Fourier — q = kAΔT/t
Substituting
$q = 0.8(188)(47)/1.1$
Evaluate
$q = 6,426 Btu/hr$

Answer:

q ≈ 6,426 Btu/hr

Why the other options are there

7,776 Btu/hr (thickness multiplied)
37.6 Btu/hr (area omitted)

Reference: FE Reference Handbook — Materials Science → Thermal Properties

Example 3

Steady heat flow through a wall — Thermal Properties (3)

A 0.9 ft thick concrete wall of area 183 ft² has k = 1.6 Btu/(hr·ft·°F) and a 82°F temperature difference. What is the heat flow rate?

Given

k = 1.6 Btu/hr·ft·°F
$A = 183 ft^{2}$
ΔT = 82°F
$t = 0.9 ft$

Find

Heat flow q

Start with the thinking

Fourier's law for a plane wall is linear in ΔT.
Thickness divides, area multiplies.

Step-by-step solution

Fourier — q = kAΔT/t
Substituting
$q = 1.6(183)(82)/0.9$
Evaluate
$q = 26,677 Btu/hr$

Answer:

q ≈ 26,677 Btu/hr

Why the other options are there

21,609 Btu/hr (thickness multiplied)
131.2 Btu/hr (area omitted)

Reference: FE Reference Handbook — Materials Science → Thermal Properties

Example 4

Steady heat flow through a wall — Thermal Properties (4)

A 0.7 ft thick concrete wall of area 199 ft² has k = 1.8 Btu/(hr·ft·°F) and a 60°F temperature difference. What is the heat flow rate?

Given

k = 1.8 Btu/hr·ft·°F
$A = 199 ft^{2}$
ΔT = 60°F
$t = 0.7 ft$

Find

Heat flow q

Start with the thinking

Fourier's law for a plane wall is linear in ΔT.
Thickness divides, area multiplies.

Step-by-step solution

Fourier — q = kAΔT/t
Substituting
$q = 1.8(199)(60)/0.7$
Evaluate
$q = 30,703 Btu/hr$

Answer:

q ≈ 30,703 Btu/hr

Why the other options are there

15,044 Btu/hr (thickness multiplied)
108.0 Btu/hr (area omitted)

Reference: FE Reference Handbook — Materials Science → Thermal Properties

Example 5

Steady heat flow through a wall — Thermal Properties (5)

A 1.2 ft thick concrete wall of area 297 ft² has k = 1.2 Btu/(hr·ft·°F) and a 47°F temperature difference. What is the heat flow rate?

Given

k = 1.2 Btu/hr·ft·°F
$A = 297 ft^{2}$
ΔT = 47°F
$t = 1.2 ft$

Find

Heat flow q

Start with the thinking

Fourier's law for a plane wall is linear in ΔT.
Thickness divides, area multiplies.

Step-by-step solution

Fourier — q = kAΔT/t
Substituting
$q = 1.2(297)(47)/1.2$
Evaluate
$q = 13,959 Btu/hr$

Answer:

q ≈ 13,959 Btu/hr

Why the other options are there

20,101 Btu/hr (thickness multiplied)
56.4 Btu/hr (area omitted)

Reference: FE Reference Handbook — Materials Science → Thermal Properties

Example 6

Steady heat flow through a wall — Thermal Properties (6)

A 1.3 ft thick concrete wall of area 218 ft² has k = 1.0 Btu/(hr·ft·°F) and a 21°F temperature difference. What is the heat flow rate?

Given

k = 1.0 Btu/hr·ft·°F
$A = 218 ft^{2}$
ΔT = 21°F
$t = 1.3 ft$

Find

Heat flow q

Start with the thinking

Fourier's law for a plane wall is linear in ΔT.
Thickness divides, area multiplies.

Step-by-step solution

Fourier — q = kAΔT/t
Substituting
$q = 1.0(218)(21)/1.3$
Evaluate
$q = 3,522 Btu/hr$

Answer:

q ≈ 3,522 Btu/hr

Why the other options are there

5,951 Btu/hr (thickness multiplied)
21.0 Btu/hr (area omitted)

Reference: FE Reference Handbook — Materials Science → Thermal Properties

Example 7

Steady heat flow through a wall — Thermal Properties (7)

A 0.8 ft thick concrete wall of area 230 ft² has k = 0.8 Btu/(hr·ft·°F) and a 47°F temperature difference. What is the heat flow rate?

Given

k = 0.8 Btu/hr·ft·°F
$A = 230 ft^{2}$
ΔT = 47°F
$t = 0.8 ft$

Find

Heat flow q

Start with the thinking

Fourier's law for a plane wall is linear in ΔT.
Thickness divides, area multiplies.

Step-by-step solution

Fourier — q = kAΔT/t
Substituting
$q = 0.8(230)(47)/0.8$
Evaluate
$q = 10,810 Btu/hr$

Answer:

q ≈ 10,810 Btu/hr

Why the other options are there

6,918 Btu/hr (thickness multiplied)
37.6 Btu/hr (area omitted)

Reference: FE Reference Handbook — Materials Science → Thermal Properties

Example 8

Steady heat flow through a wall — Thermal Properties (8)

A 1.2 ft thick concrete wall of area 214 ft² has k = 0.7 Btu/(hr·ft·°F) and a 56°F temperature difference. What is the heat flow rate?

Given

k = 0.7 Btu/hr·ft·°F
$A = 214 ft^{2}$
ΔT = 56°F
$t = 1.2 ft$

Find

Heat flow q

Start with the thinking

Fourier's law for a plane wall is linear in ΔT.
Thickness divides, area multiplies.

Step-by-step solution

Fourier — q = kAΔT/t
Substituting
$q = 0.7(214)(56)/1.2$
Evaluate
$q = 6,991 Btu/hr$

Answer:

q ≈ 6,991 Btu/hr

Why the other options are there

10,067 Btu/hr (thickness multiplied)
39.2 Btu/hr (area omitted)

Reference: FE Reference Handbook — Materials Science → Thermal Properties

Example 9

Steady heat flow through a wall — Thermal Properties (9)

A 1.0 ft thick concrete wall of area 260 ft² has k = 2.2 Btu/(hr·ft·°F) and a 66°F temperature difference. What is the heat flow rate?

Given

k = 2.2 Btu/hr·ft·°F
$A = 260 ft^{2}$
ΔT = 66°F
$t = 1.0 ft$

Find

Heat flow q

Start with the thinking

Fourier's law for a plane wall is linear in ΔT.
Thickness divides, area multiplies.

Step-by-step solution

Fourier — q = kAΔT/t
Substituting
$q = 2.2(260)(66)/1.0$
Evaluate
$q = 37,752 Btu/hr$

Answer:

q ≈ 37,752 Btu/hr

Why the other options are there

37,752 Btu/hr (thickness multiplied)
145.2 Btu/hr (area omitted)

Reference: FE Reference Handbook — Materials Science → Thermal Properties

Example 10

Steady heat flow through a wall — Thermal Properties (10)

A 1.1 ft thick concrete wall of area 191 ft² has k = 1.2 Btu/(hr·ft·°F) and a 82°F temperature difference. What is the heat flow rate?

Given

k = 1.2 Btu/hr·ft·°F
$A = 191 ft^{2}$
ΔT = 82°F
$t = 1.1 ft$

Find

Heat flow q

Start with the thinking

Fourier's law for a plane wall is linear in ΔT.
Thickness divides, area multiplies.

Step-by-step solution

Fourier — q = kAΔT/t
Substituting
$q = 1.2(191)(82)/1.1$
Evaluate
$q = 17,086 Btu/hr$

Answer:

q ≈ 17,086 Btu/hr

Why the other options are there

20,674 Btu/hr (thickness multiplied)
98.4 Btu/hr (area omitted)

Reference: FE Reference Handbook — Materials Science → Thermal Properties