Question 1

The latent heat of fusion of ice is 3.36 × 10⁵ J/kg. How much heat is needed to melt 500 g of ice at 0°C?

Accepted Answer

Q = mL = 0.5 × 3.36 × 10⁵ = 1.68 × 10⁵ J.

Question 2

The coefficient of volumetric expansion of a liquid is 5 × 10⁻⁴ /°C. What is the coefficient of linear expansion of the container if the apparent expansion remains zero when heated?

Accepted Answer

For zero apparent expansion: γ_liquid = 3α_container, so α = (5 × 10⁻⁴)/3 = 1.67 × 10⁻⁴ /°C.

Question 3

A metal rod of length 1 m at 0°C is heated to 100°C. If the coefficient of linear expansion is 12 × 10⁻⁶ /°C, what is the increase in length?

Accepted Answer

Using ΔL = αL₀ΔT = 12 × 10⁻⁶ × 1 × 100 = 1.2 × 10⁻³ m.

Question 4

A glass sphere has a radius of 10 cm at 20°C. When heated to 120°C, what is the percentage change in its surface area? (α = 1.2 × 10⁻⁵ /°C)

Accepted Answer

Percentage change in surface area = 2αΔT × 100 = 2 × 1.2 × 10⁻⁵ × 100 × 100 = 0.24%.

Question 5

The specific heat capacity of water is 4200 J/(kg·K). How much heat is required to raise the temperature of 2 kg of water from 25°C to 75°C?

Accepted Answer

Q = mcΔT = 2 × 4200 × (75 - 25) = 2 × 4200 × 50 = 4.2 × 10⁵ J.

Question 6

A copper rod of length 1 m expands by 1.7 mm when heated from 0°C to 100°C. What is the linear expansion coefficient of copper?

Accepted Answer

Using ΔL = α·L₀·ΔT, we get α = 1.7 mm / (1000 mm × 100 K) = 1.7 × 10⁻⁵ K⁻¹.

Question 7

The relationship between linear expansion coefficient (α), superficial expansion coefficient (β), and volumetric expansion coefficient (γ) is:

Accepted Answer

For small expansions, superficial expansion coefficient β relates to linear by β = 2α, and volumetric by γ = 3α.

Question 8

A concrete bridge of length 200 m is constructed at 15°C. If the linear expansion coefficient is 1.2 × 10⁻⁵ K⁻¹, what expansion gap is needed to accommodate temperature changes up to 45°C?

Accepted Answer

ΔL = 1.2 × 10⁻⁵ × 200 × (45 - 15) = 1.2 × 10⁻⁵ × 200 × 30 = 0.072 m = 0.72 cm.

Question 9

Water exhibits anomalous expansion between 0°C and 4°C. This means water's density is:

Accepted Answer

Water contracts until 4°C (density increases), then expands above 4°C, making its density maximum at 4°C.

Question 10

An aluminium sphere has a volume of 500 cm³ at 20°C. The volumetric expansion coefficient of aluminium is 7.2 × 10⁻⁵ K⁻¹. What is the volume at 120°C?

Accepted Answer

ΔV = γ·V₀·ΔT = 7.2 × 10⁻⁵ × 500 × 100 = 3.6 cm³, so final volume = 500 + 3.6 = 503.6 cm³.

Question 11

The coefficient of volumetric expansion of a liquid is 5 × 10⁻⁴ K⁻¹. If 1 litre of this liquid is heated from 20°C to 70°C, what is the approximate increase in volume?

Accepted Answer

ΔV = γ·V₀·ΔT = 5 × 10⁻⁴ × 1000 mL × 50 K = 25 mL.

Question 12

A steel ball has a radius of 10 cm at 25°C. If the linear expansion coefficient of steel is 1.2 × 10⁻⁵ K⁻¹, what is the volumetric expansion coefficient?

Accepted Answer

The volumetric expansion coefficient γ = 3α, so γ = 3 × 1.2 × 10⁻⁵ = 3.6 × 10⁻⁵ K⁻¹.

Question 13

When a glass thermometer is placed in hot water, initially the mercury level drops before rising. This phenomenon is known as:

Accepted Answer

The glass bulb expands faster initially than the mercury inside it, causing the apparent drop—this is differential expansion.

Question 14

A brass rod has a length of 2 m at 30°C. The linear expansion coefficient of brass is 1.8 × 10⁻⁵ K⁻¹. What will be its length at 80°C?

Accepted Answer

ΔL = α·L₀·ΔT = 1.8 × 10⁻⁵ × 2 × 50 = 1.8 × 10⁻³ m = 1.8 mm, so final length = 2.0018 m ≈ 2.0009 m (rounding to significant figures).

Question 15

A copper rod of length 1 m at 0°C is heated to 100°C. If the linear expansion coefficient of copper is 1.7 × 10⁻⁵ K⁻¹, what is the increase in length of the rod?

Accepted Answer

Using ΔL = L₀ × α × ΔT, we get ΔL = 1 × 1.7 × 10⁻⁵ × 100 = 1.7 × 10⁻³ m = 1.7 mm.

Question 16

A liquid has a coefficient of volumetric expansion of 5 × 10⁻⁴ K⁻¹. If 2 liters of this liquid is heated from 20°C to 70°C, what is the increase in volume?

Accepted Answer

Using ΔV = V₀ × γ × ΔT, we get ΔV = 2 × 5 × 10⁻⁴ × 50 = 0.05 L.

Question 17

The relationship between volumetric expansion coefficient (γ) and linear expansion coefficient (α) for isotropic solids is:

Accepted Answer

For an isotropic solid, volumetric expansion follows V = V₀(1 + 3αΔT) for small expansions, so γ = 3α.

Question 18

A steel ring has an inner diameter of 10 cm at 20°C. The linear expansion coefficient of steel is 1.2 × 10⁻⁵ K⁻¹. What will be the inner diameter at 120°C?

Accepted Answer

Using D = D₀(1 + αΔT), we get D = 10(1 + 1.2 × 10⁻⁵ × 100) = 10 × 1.0012 = 10.012 cm.

Agniveer Army Technical Thermal Properties of Matter

Thermal Properties of Matter — Practice Questions