Chapter 4 – Thermal Phenomenon Madhyamik Suggestion 2026

(c) Nature of the material

Explanation:

Thermal conductivity is a property of a material that determines how efficiently heat is transferred through it. It depends on the nature of the material, as different materials have different atomic structures that influence heat transfer. Factors like temperature and impurities can affect conductivity, but it does not depend on the length or cross-sectional area of the material.

(c) °C⁻¹

Explanation:

The coefficient of linear expansion (α) is defined as the increase in length per unit length per degree rise in temperature. Its unit is derived as:

α = (change in length) / (original length × temperature change)
Since length cancels out, the unit becomes per degree Celsius (°C⁻¹) or per Kelvin (K⁻¹).

(c) Three

Explanation:

Solids expand in three ways when heated:

1. Linear Expansion (α) – Expansion in length
2. Surface Expansion (β) – Expansion in area
3. Volume Expansion (γ) – Expansion in volume

These three coefficients are interrelated as β = 2α and γ = 3α.

(a) Silver

Explanation:

Among the given options, silver is the best conductor of heat due to its free electrons, which transfer heat efficiently. Although diamond has high thermal conductivity, it is a non-metal and is primarily used in specialized applications rather than general heat conduction. The thermal conductivity of silver (406 W/m·K) is higher than that of copper (385 W/m·K) and aluminium (205 W/m·K).

(c) γr = γv

Explanation:

Apparent expansion of a liquid is given by:

γa = γr – γv

where γr is the real expansion of the liquid and γv is the expansion of the container. If γr = γv, then γa = 0, meaning no apparent expansion is observed. This happens when the liquid and the container expand at the same rate.

(b) β = 2α

Explanation:

The relationship between thermal expansion coefficients is:

• β (surface expansion) = 2α
• γ (volume expansion) = 3α

Thus, the correct answer is β = 2α.

(c) Gas

Explanation:

For gases, the coefficient of volume expansion (γg) is approximately 1/273 per °C, which remains nearly constant at all temperatures under constant pressure. For solids and liquids, expansion depends on the material properties and is not constant.

(a) K⁻¹, K⁻¹

Explanation:

Both volume expansion (γ) and surface expansion (β) measure the change in size per degree temperature change, so both have the unit K⁻¹ or °C⁻¹.

(a) 9αF = 5αC

Explanation:

Since the Fahrenheit scale is related to the Celsius scale by:
ΔT°F = (9/5) ΔT°C, the coefficient of expansion follows the same relationship:

αF = (9/5) αC, or 9αF = 5αC.

(d) Watt⁻¹ kelvin⁻¹

Explanation:

Thermal resistance (R) is the opposition to heat flow and is given by:
R = L / kA (where L is thickness, k is thermal conductivity, and A is area).
Its unit is (m·K) / W, which simplifies to W⁻¹ K⁻¹.

(a) l₁α₁ = l₂α₂

Explanation:

For the difference in length to remain constant, both rods must expand by the same proportion. This is satisfied when l₁α₁ = l₂α₂.

(b) d / kA

(c) Infinity

Explanation:

An ideal conductor has zero thermal resistance, meaning infinite thermal conductivity.

Real expansion coefficient

W m⁻¹ K⁻¹

False

Invar

False

Thermal resistance is inversely proportional to thermal conductivity.

False

K⁻¹

Coefficient of real expansion

3.66 × 10⁻³ per Kelvin

The coefficient of linear expansion does not change whether expressed in degree Celsius inverse or Kelvin inverse.

αC = αK

[M¹ L¹ T⁻³ θ⁻¹]

γr = γ a + γv

Yes, the expansion will be the same for both the hollow and solid sphere.

[M⁰ L⁰ T⁰ θ⁻¹]

β = y / (z × x)

Water is a liquid that shows anomalous expansion.

If β = x°C⁻¹, then:

γ = 3x°C⁻¹

The coefficient of volume expansion (γ) of an ideal gas at constant pressure is given by:

γ = 1/273 per °C = 3.66 × 10⁻³ per K

This means that for every 1°C rise in temperature, the volume of a gas increases by 1/273 of its initial volume at 0°C, assuming constant pressure.

1. Both heat conduction and electrical conduction occur due to the movement of free electrons in metals.
2. Both processes follow laws similar to Ohm’s law, where the rate of heat flow is proportional to the temperature difference, just as current is proportional to voltage difference.

A non-metal with high thermal conductivity is diamond.

Thermal conductivity (k) is the property of a material that determines its ability to conduct heat. It is defined as the amount of heat transferred per unit time through a unit area of a material per unit temperature gradient.

SI unit of thermal conductivity: W m⁻¹ K⁻¹ (watt per meter per Kelvin)

The coefficient of surface expansion (β) is the increase in surface area per unit area per degree rise in temperature.

Mathematically, β = (ΔA) / (A × ΔT), where ΔA is the change in surface area, A is the original surface area, and ΔT is the temperature change.

SI unit: K⁻¹ or °C⁻¹

In the definition of the volume expansion coefficient of a gas, the pressure is kept constant.

A non-metal that is a good conductor of heat is diamond.

The coefficient of linear expansion of copper being 17 × 10⁻⁶ /°C means that for every 1°C rise in temperature, the length of copper increases by 17 × 10⁻⁶ times its original length.

This value remains the same in the Kelvin scale because 1°C rise in temperature is equal to 1 K rise in temperature, so the expansion remains unchanged.

An example of volume expansion in a liquid is water expanding when heated.

The coefficient of area expansion (β) is given by:
β = (A₂ – A₁) / (A₁ × (T₂ – T₁))

SI unit: K⁻¹ or °C⁻¹

The three factors on which conduction of heat through a solid substance depends are:

• Nature of the material – Metals conduct heat better than non-metals.
• Temperature difference – Greater temperature differences cause faster heat transfer.
• Thickness of the material – Thicker materials resist heat flow more.

The coefficient of linear expansion (α) is the increase in length per unit length per degree rise in temperature.

For copper, α = 17 × 10⁻⁶ °C⁻¹, meaning for every 1°C rise in temperature, the length of copper increases by 17 × 10⁻⁶ times its original length.

Thermal conductivity (k) is the ability of a material to conduct heat.

For an ideal insulator, the thermal conductivity should be zero, meaning no heat transfer occurs.

The rate of heat transfer depends on:

1. Thermal conductivity (k) – More conductivity, more heat transfer.
2. Temperature difference (ΔT) – Greater ΔT leads to faster heat transfer.
3. Thickness of the material (L) – More thickness, less transfer.
4. Surface area (A) – Larger area, more heat transfer.

The coefficient of apparent expansion (γa) of a liquid is the observed increase in volume per unit volume per degree rise in temperature, when the liquid is heated inside a container.

Apparent expansion of a liquid depends on:

1. Material of the container: higher container expansion means lower apparent expansion.
2. Nature of the liquid: different liquids expand differently.
3. Temperature change: higher temperature rise increases expansion.
4. Initial volume of the liquid: larger volume shows more expansion.

The iron chair feels hotter because iron is a good conductor of heat, transferring heat quickly to the hand. Wood, being a poor conductor, does not conduct heat well and feels cooler.

Thermostats are used in electrical appliances like refrigerators, ovens, and air conditioners to control temperature.

The change in length (delta L) is directly proportional to the initial length (L₀) and the temperature change (ΔT).

γa is always less than γr.

Thermal resistance (R) is given by:

R = L / (k × A)

For R = 1/k,
L / (k × A) = 1 / k

This happens only if L = A, which is rare. In general, R is inversely proportional to k.

If k increases, R decreases, and if k decreases, R increases.

Thermal resistance (R) is the opposition to heat flow in a material.

Surface expansion depends on:

1. Material properties
2. Temperature change
3. Original surface area

No, because if γr = γv, the apparent expansion would be zero, meaning the liquid level would not change with temperature, making measurement impossible.

Since R is inversely proportional to k (R ∝ 1 / k), we take the inverse of the given ratio of k:

R₁ : R₂ = k₂ : k₁

Substituting the values from the given ratio k₁ : k₂ = 1 : 4, we get:

R₁ : R₂ = 4 : 1

Change in length (ΔL) = 100.06 – 100 = 0.06 cm

Change in temperature (ΔT) = 75°C – 25°C = 50°C

Initial Length (L₀) = 100 cm

α = (ΔL) / (L₀ × ΔT)

= (0.06) / (100 × 50)

= 1.2 × 10⁻⁵ °C⁻¹.

The coefficient of apparent expansion (γa) of a liquid depends on both the real expansion (γr) of the liquid and the expansion of the container (γv).

Since gamma a is inversely related to gamma v, the apparent expansion will be more in the container that expands less.