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Thermal Physics

Thermal Physics: Thermal Insulators and Heat Conduction

Thermal insulators are materials characterized by a low thermal conductivity that significantly impede the transfer of heat energy through conduction. In molecular terms, they possess tightly bound valence electrons and lack free charge carriers, restricting heat transport primarily to lattice vibrations (phonons).

UP TGT ScienceUP PGT PhysicsStudy Notes + Practice

Scope and prerequisites

TGT core

Basic definitions of thermal conductivity, distinction between conductors and insulators, steady-state heat flow through slabs, and temperature gradient concepts.

PGT extension

Microscopic phonon theory of thermal insulation in non-metals, Debye-Einstein specific heat models contributing to conductivity, cylindrical and spherical radial heat flow, and thermal resistance networks.

Prerequisites

Concept of Temperature
Kinetic theory of gases
Law of equipartition of energy

Microscopic Mechanism of Heat Conduction in Insulators

In electrical and thermal insulators, heat conduction occurs almost exclusively via lattice vibrations or quantized elastic waves known as phonons.
Due to the absence of free electrons, the electronic contribution to thermal conductivity (kappa_e) is negligible compared to the lattice contribution (kappa_l).
Phonon-phonon scattering, particularly Umklapp processes, provides the primary thermal resistance mechanism at high temperatures.

Fourier's Law of Heat Conduction

The rate of heat flow through a uniform slab is directly proportional to the cross-sectional area and the temperature gradient normal to the surface.
Mathematically expressed as dQ/d$t = -kA (dT/dx)$, where k is the coefficient of thermal conductivity.
The negative sign indicates that heat flows in the direction of decreasing temperature.

Thermal Resistance and Composite Slabs

Thermal resistance R_th for a slab of thickness L, area A, and conductivity k is defined as L / (kA).
For series combinations of insulating layers, thermal resistances are additive: R_eq = R₁ + R₂ + ...
For parallel combinations, the reciprocal of equivalent thermal resistance is the sum of reciprocals of individual thermal resistances.

Temperature Gradient in Steady State

In the steady-state condition, no heat is absorbed or liberated by any intermediate layer of the insulator; the temperature profile across a flat slab is linear.
The temperature gradient (dT/dx) remains constant throughout a homogeneous flat slab of uniform cross-section.
For cylindrical insulators (like pipe lagging), the temperature profile is logarithmic rather than linear.

Derivations

Radial Heat Flow through a Cylindrical Insulator

Conditions: Steady-state heat flow radially outward through a long hollow cylinder of inner radius r₁, outer radius r₂, length l, and thermal conductivity k.

Consider a coaxial cylindrical shell of radius r and thickness dr within the insulator.
Apply Fourier's law for radial heat flow: dQ/d$t = -kA(dT/dr) = -k(2\pirl)(dT/dr)$.
Separate variables for integration: (dQ/dt) * (dr/r) = -2πkl dT.
Integrate from inner radius r₁ (temperature T₁) to outer radius r₂ (temperature T₂): (dQ/dt) * ln(r₂/r₁) = 2πkl(T₁ - T₂).

Result: dQ/d$t = 2\pikl(T_{1} - T_{2}) / [\ln(r_{2}/r_{1})]$

Equivalent Thermal Conductivity of Composite Slabs in Series

Conditions: Two slabs of thicknesses L₁, L₂, conductivities k₁, k₂, and identical cross-sectional area A placed in series.

Let T₁, T, and T₂ be the temperatures at the outer face of slab 1, the interface, and the outer face of slab 2 respectively.
In steady state, the rate of heat flow H is the same through both slabs: $H = k_{1}A(T_{1} - T)/L_{1} = k_{2}A(T - T_{2})/L_{2}$.
Express temperature drops: (T₁ - T) = H L₁ / (k₁A) and (T - T₂) = H L₂ / (k₂A).
Add the temperature drops to get total drop T₁ - T₂ = H [ (L₁/k₁A) + (L₂/k₂A) ]. Define equivalent conductivity k_eq for total thickness L₁ + L₂.

Result: k_eq = (L₁ + L₂) / [ (L₁/k₁) + (L₂/k₂) ]

Formula sheet

Formula / law	Equation	Variables and units	Conditions
Fourier's Law of Heat Conduction	$$\frac{dQ}{dt} = -kA \frac{dT}{dx}$$	Q = Heat, t = time, k = thermal conductivity, A = area, T = temperature, x = position W (Watts)	Isotropic medium, steady state
Thermal Resistance (Linear)	$$R_{th} = \frac{L}{kA}$$	L = thickness, k = thermal conductivity, $A = cross-sectional area$ K/W or °C/W	Uniform cross-section, flat slab
Thermal Resistance (Cylindrical)	$$R_{th} = \frac{\ln(r_2/r_1)}{2\pi kl}$$	r₁ = inner radius, r₂ = outer radius, l = length, k = thermal conductivity K/W	Radial heat flow through hollow cylinder
Temperature Gradient	$$\frac{dT}{dx} = \frac{T_2 - T_1}{L}$$	T₁, T₂ = temperatures of faces, L = slab thickness K/m	Uniform flat slab in steady state
Series Combination of Thermal Resistances	$$R_{eq} = R_1 + R_2 + R_3 + \dots$$	R_i = thermal resistance of individual layers K/W	Perfect thermal contact between layers
Parallel Combination of Thermal Resistances	$$\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \dots$$	R_i = thermal resistance of parallel branches W/K	Faces kept at same temperature extremities
Ingenhousz's Experiment Relation	$$\frac{k_1}{k_2} = \frac{l_1^2}{l_2^2}$$	l₁, l₂ = lengths of melted wax on rods of same diameter Dimensionless ratio	Identical cross-section, exposed to same temperature bath
Phonon Mean Free Path Dependence	$$k_l = \frac{1}{3} C_v v \lambda$$	C_v = heat capacity per unit volume, v = phonon velocity, $\lambda = phonon mean free path$ W/(m·K)	Debye approximation for non-metals

Graphs and experiments

Temperature Profile Across a Flat Insulating Slab

Draw: A linear graph of Temperature (T on y-axis) versus Distance (x on x-axis) with a negative constant slope.

Interpret: In steady-state conduction through a homogeneous insulator, the temperature drops uniformly and linearly from the hot face to the cold face.

Exam use: Tested in conceptual questions regarding temperature gradients and multi-layer wall insulation.

Ingenhousz's Experiment (Thermal Conductivity of Rods)

Draw: Coated rods of different materials dipped in a hot wax bath, showing varying lengths of melted wax along each rod.

Interpret: The length of melted wax l is proportional to the square root of thermal conductivity (k ∝ l²).

Exam use: Direct TGT formula-based numericals and conceptual comparisons between conductors and insulators.

Thermal Conductivity vs. Temperature for Insulators

Draw: A curve showing k rising steeply at low temperatures (due to increase in specific heat), peaking, and then decreasing at higher temperatures as phonon scattering (Umklapp) dominates.

Interpret: Unlike metals where electronic thermal conductivity decreases with temperature, lattice thermal conductivity in insulators exhibits a pronounced Debye temperature peak.

Exam use: PGT level theoretical questions on phonon-mediated heat transport behavior.

Solved numericals

TGT core

A flat glass window of thermal conductivity 0.8 W/(m·K) has an area of 2 m² and a thickness of 0.5 cm. If the inner and outer surface temperatures are 20 °C and 0 °C respectively, calculate the rate of heat flow through the window.

Identify given parameters: $k = 0.8 W/(m·K)$, $A = 2 m^{2}$, L = 0.5 cm = 0.005 m, Δ$T = 20 - 0 = 20 K$.
Substitute values into Fourier's law equation: dQ/d$t = k A (T_{1} - T_{2}) / L$.
dQ/d$t = (0.8 * 2 * 20) / 0.005$.
dQ/d$t = 32 / 0.005 = 6400 W$.

Answer: 6400 W

PGT extension

A composite cylindrical pipe of length 2 m has an inner insulating layer of radius 1 cm and thermal conductivity 0.1 W/(m·K), and an outer insulating layer of radius 2 cm and thermal conductivity 0.4 W/(m·K). If the inner surface is at 100 °C and the outer surface is at 20 °C, find the steady-state rate of heat flow.

Calculate thermal resistance of the first layer: R₁ = ln(r₂/r₁) / (2π k₁ l) = ln(1.5 / 1.0) / (2 * π * 0.1 * 2) [assuming intermediate radius 1.5 cm for layering, or use inner=1, interface=1.5, outer=2]. Let interface be r_i = 1.5 cm.
R₁ = ln(1.5/1.0) / (0.4 π) = 0.4055 / (1.256) = 0.322 K/W.
Calculate thermal resistance of second layer: R₂ = ln(2.0/1.5) / (2 * π * 0.4 * 2) = 0.2877 / (3.2 * π) = 0.2877 / $10.05 = 0.0286 K/W$.
Total thermal resistance R_eq = R₁ + R₂ = 0.322 + $0.0286 = 0.3506 K/W$.
Heat flow rate $H = (T_{1} - T_{2}) / R_{eq} = (100 - 20) / 0.3506 = 80 / 0.3506 \approx 228.18 W$.

Answer: 228.18 W

TGT core

Two identical insulating slabs are placed in series. Their thermal conductivities are k and 2k. What is the equivalent thermal conductivity of the combination?

Let the thickness of each slab be L and cross-sectional area be A.
Use the equivalent conductivity formula for two slabs in series: k_eq = (L₁ + L₂) / [ (L₁/k₁) + (L₂/k₂) ].
Substitute L₁ = L₂ = L, k₁ = k, and k₂ = 2k: k_eq = (L + L) / [ (L/k) + (L/2k) ].
Simplify the expression: k_eq = 2L / [ (L/k)(1 + 1/2) ] = 2 / (1.5 / k) = (4/3)k.

Answer: (4/3)k

Assumptions and limitations

Steady-state condition is assumed, meaning temperatures at all points within the insulator do not change with time.
Heat flow is strictly one-dimensional or follows simplified symmetric geometry (planar or radial), ignoring edge effects.
Thermal conductivity k is treated as constant across the temperature range, although real insulators show temperature-dependent k variations.

Common misconceptions

Common error: Insulators can completely stop the flow of heat.

Correct: Insulators only reduce the rate of heat flow, they cannot block it entirely as long as a temperature difference exists.

Zero heat flow requires infinite thermal resistance, which does not exist in real physical materials.

Common error: The temperature gradient is steeper in the material with higher thermal conductivity.

Correct: The temperature gradient is steeper in the material with lower thermal conductivity (the insulator).

From Fourier's law, dT/d$x = -H / (kA);$ for a given heat flux H and area A, the temperature gradient is inversely proportional to k.

Quick revision

Thermal insulators have negligible electronic thermal conductivity; heat transfer is governed by phonons.
Fourier's Law: dQ/d$t = -kA(dT/dx); the negative sign denotes heat flow down the temperature gradient$.
Thermal resistance of a flat slab is given by R_th = L / (kA).
In series combinations of insulating slabs, thermal resistances add algebraically.
Ingenhousz's experiment relates thermal conductivity to the square of the melted wax length: k ∝ l².

Must remember

In electrical and thermal insulators, heat conduction occurs predominantly via lattice vibrations known as phonons.
Fourier's law of heat conduction is expressed mathematically as $\frac{dQ}{dt} = -kA \frac{dT}{dx}$.
Thermal resistance $R_{th}$ for a flat slab of thickness $L$, area $A$, and conductivity $k$ is given by $R_{th} = \frac{L}{kA}$.
For series combinations of thermal resistances, the equivalent thermal resistance is the sum: $R_{eq} = R_1 + R_2 + \dots$.
In steady state, the temperature profile across a homogeneous flat slab is linear, while across a cylindrical insulator it is logarithmic.

Glossary

PhononQuantized elastic wave representing lattice vibrations in solid insulators.

Umklapp ProcessA phonon-phonon scattering process that does not conserve crystal momentum and provides the primary thermal resistance at high temperatures.

Thermal Conductivity ($k$)A material property indicating its ability to conduct heat, measured in $W/(m \cdot K)$.

Thermal Resistance ($R_{th}$)Opposition offered by a body to the flow of heat, measured in $K/W$.

Temperature GradientRate of change of temperature with respect to position, $\frac{dT}{dx}$.

Conductors vs Insulators Heat Conduction

Parameter	Electrical & Thermal Conductors	Thermal Insulators
Primary Heat Carrier	Free electrons	Lattice vibrations (Phonons)
Electronic Contribution ($k_e$)	Dominant	Negligible
Lattice Contribution ($k_l$)	Secondary	Primary

Temperature Profile Geometry

Geometry	Temperature Profile	Temperature Gradient Expression
Flat Slab	Linear	$\frac{T_2 - T_1}{L}$
Cylindrical Pipe Lagging	Logarithmic	Depends inversely on radial distance $r$

Practice Quiz

Choose an option to reveal the explanation.

1. In electrical and thermal insulators, heat conduction occurs almost exclusively via which of the following?

Explanation: Due to the absence of free electrons in insulators, heat conduction is dominated by phonons (lattice vibrations).

2. What provides the primary thermal resistance mechanism at high temperatures in non-metal insulators?

Explanation: At high temperatures, phonon-phonon scattering via Umklapp processes limits the phonon mean free path and increases thermal resistance.

3. According to Fourier's law of heat conduction, the rate of heat flow $\frac{dQ}{dt}$ is proportional to which of the following?

Explanation: Fourier's law states that $\frac{dQ}{dt} = -kA \frac{dT}{dx}$, where $\frac{dT}{dx}$ is the temperature gradient normal to the surface.

4. Why is there a negative sign in Fourier's law equation: $\frac{dQ}{dt} = -kA \frac{dT}{dx}$?

Explanation: The negative sign indicates that heat flows down the temperature gradient, i.e., from higher to lower temperature.

5. What is the formula for the thermal resistance $R_{th}$ of a flat slab of thickness $L$, area $A$, and thermal conductivity $k$?

Explanation: Thermal resistance for a flat uniform slab is defined as $R_{th} = \frac{L}{kA}$.

6. How are thermal resistances combined when insulating layers are arranged in series?

Explanation: For series combinations of insulating layers, thermal resistances add directly: $R_{eq} = R_1 + R_2 + \dots$

7. What is the nature of the temperature profile across a homogeneous flat slab of uniform cross-section in steady state?

Explanation: In steady state, the temperature gradient is constant across a flat slab, resulting in a linear temperature profile.

8. What is the nature of the temperature profile across a cylindrical insulator (like pipe lagging) in steady state?

Explanation: For cylindrical geometry with radial heat flow, the temperature profile is logarithmic.

9. In which material is the temperature gradient steeper for a given heat flux $H$ and area $A$?

Explanation: Since $\frac{dT}{dx} = -\frac{H}{kA}$, for a given heat flux, the temperature gradient is inversely proportional to $k$, meaning it is steeper in the insulator.

10. Which relation expresses the lattice thermal conductivity in terms of phonon properties according to the Debye approximation?

Explanation: From kinetic theory applied to phonons, $k_l = \frac{1}{3} C_v v \lambda$, where $C_v$ is heat capacity per unit volume, $v$ is phonon velocity, and $\lambda$ is the phonon mean free path.

11. What is the unit of coefficient of thermal conductivity $k$ in SI units?

Explanation: From Fourier's law, $k = \frac{dQ/dt}{A (dT/dx)}$, yielding units of Watts per meter Kelvin ($W/(m \cdot K)$).

12. In Ingenhousz's experiment, if $l_1$ and $l_2$ are the lengths of melted wax on two rods of identical diameter exposed to the same temperature bath, how are their thermal conductivities related?

Explanation: Ingenhousz's relation for rods coated with wax states that $\frac{k_1}{k_2} = \frac{l_1^2}{l_2^2}$ under steady-state conduction conditions.

13. Can an insulator completely stop the flow of heat?

Explanation: Insulators reduce heat transfer rates but cannot block heat entirely unless the temperature difference is zero or thermal resistance is infinite.

14. What happens to the thermal resistance of a composite slab when two slabs are connected in parallel?

Explanation: For parallel thermal resistances, $\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \dots$

15. What is the steady-state condition regarding intermediate layers of a heat-conducting insulator slab?

Explanation: In steady state, temperatures at every point remain constant with time, meaning intermediate layers absorb or liberate net zero heat.

PYQ Patterns

These are pattern-based practice questions. Authentic year labels are only used when verified from a source.

1. Two insulating slabs of thicknesses $L_1$ and $L_2$ and thermal conductivities $k_1$ and $k_2$ with identical cross-sectional area $A$ are placed in series. What is the equivalent thermal resistance of the combination?

Explanation: In series, thermal resistances are additive: $R_{eq} = R_1 + R_2 = \frac{L_1}{k_1 A} + \frac{L_2}{k_2 A}$.

2. The temperature gradient across a flat insulating slab of thickness $0.1\text{ m}$ whose outer faces are maintained at $100^{\circ}\text{C}$ and $20^{\circ}\text{C}$ in steady state is:

Explanation: Temperature gradient $\frac{dT}{dx} = \frac{T_2 - T_1}{L} = \frac{100 - 20}{0.1} = \frac{80}{0.1} = 800\text{ K/m}$.

3. In non-metal thermal insulators, the lattice thermal conductivity $k_l$ at very low temperatures (approaching absolute zero) is proportional to:

Explanation: At low temperatures, specific heat $C_v \propto T^3$ while phonon mean free path is limited by crystal boundaries (constant), making $k_l \propto T^3$.

4. A hollow cylindrical pipe of inner radius $r_1$ and outer radius $r_2$, length $l$, and thermal conductivity $k$ has a thermal resistance of:

Explanation: Integration for radial heat flow in a hollow cylinder yields $R_{th} = \frac{\ln(r_2/r_1)}{2\pi kl}$.

5. If the thermal conductivity of an insulator is halved while its thickness is doubled, what happens to the rate of heat flow through the slab for the same temperature difference?

Explanation: Heat flow rate $H = \frac{kA \Delta T}{L}$. If $k$ becomes $k/2$ and $L$ becomes $2L$, then $H' = \frac{(k/2) A \Delta T}{2L} = \frac{1}{4} H$.

6. Which of the following mechanisms is primarily responsible for heat transport in electrical insulators?

Explanation: Electrical insulators lack free electrons, so heat transport is primarily carried out by lattice vibrations (phonons).

Timed Topic Test

Attempt these questions under a ten-minute limit using a separate timer.

1. What is the equivalent thermal resistance when three identical insulating slabs, each of thermal resistance $R$, are connected in series?

Explanation: For series combination, resistances add directly: $R_{eq} = R + R + R = 3R$.

2. The temperature gradient in a homogeneous flat slab of uniform cross-section in steady state is:

Explanation: In a homogeneous flat slab under steady state, the temperature gradient $\frac{dT}{dx}$ remains constant throughout.

3. Umklapp phonon scattering processes are distinguished by the fact that:

Explanation: Umklapp processes do not conserve crystal momentum (it changes by a reciprocal lattice vector $G$), providing thermal resistance.

4. Two parallel insulating plates of areas $A_1$ and $A_2$, thicknesses $L_1$ and $L_2$, and conductivities $k_1$ and $k_2$ are placed such that their faces are kept at the same temperature extremities. The equivalent thermal conductance ($1/R_{eq}$) is:

Explanation: For parallel thermal networks, conductances are additive: $\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} = \frac{k_1 A_1}{L_1} + \frac{k_2 A_2}{L_2}$.

5. According to the phonon gas model, if the phonon mean free path $\lambda$ decreases due to increased impurity scattering at very high defect concentrations, what happens to thermal conductivity $k_l$?

Explanation: Since $k_l = \frac{1}{3} C_v v \lambda$, a decrease in $\lambda$ due to increased impurity scattering leads to a decrease in thermal conductivity.

6. What is the unit of thermal resistance $R_{th}$?

Explanation: Thermal resistance is defined as $\frac{\Delta T}{dQ/dt}$, giving units of Kelvin per Watt ($K/W$).

7. In a steady-state heat conduction experiment across a flat slab, if the heat input is doubled, what happens to the temperature gradient across the slab?

Explanation: From Fourier's law $\frac{dQ/dt}{A} = -k \frac{dT}{dx}$, heat flux is directly proportional to the temperature gradient; doubling heat input doubles the gradient.

8. Why do metals generally have much higher thermal conductivity than non-metallic insulators?

Explanation: Free electrons in metals transport thermal energy rapidly (Wiedemann-Franz law), giving them massive electronic thermal conductivity compared to insulators.

9. A composite wall consists of two layers of equal thickness $L$ and conductivities $k$ and $2k$. What is the effective thermal conductivity of the combination for heat flow normal to the layers (series)?

Explanation: $R_{eq} = \frac{L}{kA} + \frac{L}{(2k)A} = \frac{3L}{2kA}$. Also $R_{eq} = \frac{2L}{k_{eff} A}$. Equating gives $\frac{2}{k_{eff}} = \frac{3}{2k} \implies k_{eff} = \frac{4}{3}k$.

10. Which of the following statements is correct regarding the temperature profile in cylindrical pipe insulation?

Explanation: Integrating the heat conduction equation in cylindrical coordinates yields a logarithmic temperature profile.

Thermal Physics: Thermal Insulators and Heat Conduction

Scope and prerequisites

TGT core

PGT extension

Prerequisites

Microscopic Mechanism of Heat Conduction in Insulators

Fourier's Law of Heat Conduction

Thermal Resistance and Composite Slabs

Temperature Gradient in Steady State

Derivations

Radial Heat Flow through a Cylindrical Insulator

Equivalent Thermal Conductivity of Composite Slabs in Series

Formula sheet

Graphs and experiments

Temperature Profile Across a Flat Insulating Slab

Ingenhousz's Experiment (Thermal Conductivity of Rods)

Thermal Conductivity vs. Temperature for Insulators

Solved numericals

A flat glass window of thermal conductivity 0.8 W/(m·K) has an area of 2 m2 and a thickness of 0.5 cm. If the inner and outer surface temperatures are 20 °C and 0 °C respectively, calculate the rate of heat flow through the window.

Two identical insulating slabs are placed in series. Their thermal conductivities are k and 2k. What is the equivalent thermal conductivity of the combination?

Assumptions and limitations

Common misconceptions

Quick revision

Must remember

Glossary

Conductors vs Insulators Heat Conduction

Temperature Profile Geometry

Practice Quiz

1. In electrical and thermal insulators, heat conduction occurs almost exclusively via which of the following?

2. What provides the primary thermal resistance mechanism at high temperatures in non-metal insulators?

3. According to Fourier's law of heat conduction, the rate of heat flow $\frac{dQ}{dt}$ is proportional to which of the following?

4. Why is there a negative sign in Fourier's law equation: $\frac{dQ}{dt} = -kA \frac{dT}{dx}$?

5. What is the formula for the thermal resistance $R_{th}$ of a flat slab of thickness $L$, area $A$, and thermal conductivity $k$?

6. How are thermal resistances combined when insulating layers are arranged in series?

7. What is the nature of the temperature profile across a homogeneous flat slab of uniform cross-section in steady state?

8. What is the nature of the temperature profile across a cylindrical insulator (like pipe lagging) in steady state?

9. In which material is the temperature gradient steeper for a given heat flux $H$ and area $A$?

10. Which relation expresses the lattice thermal conductivity in terms of phonon properties according to the Debye approximation?

11. What is the unit of coefficient of thermal conductivity $k$ in SI units?

12. In Ingenhousz's experiment, if $l_1$ and $l_2$ are the lengths of melted wax on two rods of identical diameter exposed to the same temperature bath, how are their thermal conductivities related?

13. Can an insulator completely stop the flow of heat?

14. What happens to the thermal resistance of a composite slab when two slabs are connected in parallel?

15. What is the steady-state condition regarding intermediate layers of a heat-conducting insulator slab?

PYQ Patterns

1. Two insulating slabs of thicknesses $L_1$ and $L_2$ and thermal conductivities $k_1$ and $k_2$ with identical cross-sectional area $A$ are placed in series. What is the equivalent thermal resistance of the combination?

2. The temperature gradient across a flat insulating slab of thickness $0.1\text{ m}$ whose outer faces are maintained at $100^{\circ}\text{C}$ and $20^{\circ}\text{C}$ in steady state is:

3. In non-metal thermal insulators, the lattice thermal conductivity $k_l$ at very low temperatures (approaching absolute zero) is proportional to:

4. A hollow cylindrical pipe of inner radius $r_1$ and outer radius $r_2$, length $l$, and thermal conductivity $k$ has a thermal resistance of:

5. If the thermal conductivity of an insulator is halved while its thickness is doubled, what happens to the rate of heat flow through the slab for the same temperature difference?

6. Which of the following mechanisms is primarily responsible for heat transport in electrical insulators?

Timed Topic Test

1. What is the equivalent thermal resistance when three identical insulating slabs, each of thermal resistance $R$, are connected in series?

2. The temperature gradient in a homogeneous flat slab of uniform cross-section in steady state is:

3. Umklapp phonon scattering processes are distinguished by the fact that:

4. Two parallel insulating plates of areas $A_1$ and $A_2$, thicknesses $L_1$ and $L_2$, and conductivities $k_1$ and $k_2$ are placed such that their faces are kept at the same temperature extremities. The equivalent thermal conductance ($1/R_{eq}$) is:

5. According to the phonon gas model, if the phonon mean free path $\lambda$ decreases due to increased impurity scattering at very high defect concentrations, what happens to thermal conductivity $k_l$?

6. What is the unit of thermal resistance $R_{th}$?

7. In a steady-state heat conduction experiment across a flat slab, if the heat input is doubled, what happens to the temperature gradient across the slab?

8. Why do metals generally have much higher thermal conductivity than non-metallic insulators?

9. A composite wall consists of two layers of equal thickness $L$ and conductivities $k$ and $2k$. What is the effective thermal conductivity of the combination for heat flow normal to the layers (series)?

10. Which of the following statements is correct regarding the temperature profile in cylindrical pipe insulation?

A flat glass window of thermal conductivity 0.8 W/(m·K) has an area of 2 m² and a thickness of 0.5 cm. If the inner and outer surface temperatures are 20 °C and 0 °C respectively, calculate the rate of heat flow through the window.