Chapter 10: Thermal Properties of Matter Long Questions | physics Class 11 CBSE

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Chapter 10: Thermal Properties of Matter Long Questions | physics Class 11 CBSE | ByteNotes.in

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Question 1

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Describe the construction and working of a constant-volume gas thermometer. How does it establish the concept of absolute temperature, and what is the significance of –273.15°C?

A constant-volume gas thermometer measures temperature by keeping the volume of a gas constant and reading temperature in terms of pressure; a plot of P versus T is linear.
At low densities, all gases give the same pressure-temperature relationship regardless of the type of gas used, making the gas thermometer a universal standard.
Extrapolating the linear P-T graph to zero pressure gives the same temperature, –273.15°C, for all gases, regardless of the gas used or its initial pressure.
This temperature, –273.15°C, is called absolute zero; it represents the theoretical minimum temperature at which the gas would have zero pressure if it remained gaseous.
The Kelvin (absolute) temperature scale uses absolute zero as its origin (0 K), with the same unit size as the Celsius scale: T(K) = tC + 273.15.
This scale is of fundamental importance because the ideal gas equation PV = μRT requires T in Kelvin; negative temperatures are physically impossible on this scale.

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Question 2

Long Form

Derive the relation αV = 3αl for an isotropic solid. Hence explain what happens when the thermal expansion of a steel rail is completely prevented, calculating the thermal stress for a 10°C rise.

Consider a cube of side l; when temperature rises by ΔT, each side increases by Δl = αlΔT, where αl is the coefficient of linear expansion.
New volume = (l + Δl)³ = l³ + 3l²Δl + 3l(Δl)² + (Δl)³; neglecting higher-order terms in Δl (which are very small), ΔV ≈ 3l²Δl = 3l³αlΔT.
Therefore αV = (ΔV/V)/ΔT = 3αl, establishing the relation between volume and linear expansivities.
When a steel rail's expansion is prevented, external compressive forces from rigid supports create a compressive strain equal to αlΔT in the rail.
The thermal stress developed = Y × αl × ΔT = 2×10¹¹ × 1.2×10⁻⁵ × 10 = 2.4×10⁷ N m⁻², which is very large.
Such thermal stresses in railway tracks can easily bend the rails; this is why gaps are intentionally left between rail sections to allow for free thermal expansion.

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Question 3

Long Form

Explain the anomalous expansion of water between 0°C and 4°C. Discuss its environmental consequences for aquatic life and illustrate using the density-temperature graph described in the chapter.

Unlike most substances, water contracts when heated between 0°C and 4°C, meaning its volume decreases and density increases as temperature rises from 0°C to 4°C.
Below 4°C, the volume of water increases with decreasing temperature, so density decreases; water therefore has its maximum density at 4°C.
When a lake or pond cools in winter, surface water loses heat to the atmosphere, becomes denser, and sinks; warmer, less dense water from below rises to replace it.
This convective mixing continues until the entire water body reaches 4°C; further cooling of surface water below 4°C makes it less dense, so it stays at the surface.
The less dense surface water freezes first; the layer of ice formed acts as an insulator, preventing further rapid cooling of deeper water where aquatic life exists.
If water did not have this anomalous property, lakes would freeze from the bottom up, destroying virtually all aquatic plant and animal life during winter.

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Question 4

Long Form

Derive an expression for the coefficient of area expansion of a rectangular solid in terms of its linear expansivity. Show that the coefficient of area expansion is approximately twice the linear expansivity.

Consider a rectangular sheet of a solid with length a and breadth b at temperature T; when temperature increases by ΔT, a increases by Δa = αla·ΔT and b by Δb = αlb·ΔT.
The increase in area: ΔA = ΔA₁ + ΔA₂ + ΔA₃ = a(Δb) + b(Δa) + (Δa)(Δb) = aαlbΔT + bαlaΔT + αl²ab(ΔT)².
Simplifying: ΔA = αlabΔT(2 + αlΔT) = αlAΔT(2 + αlΔT), where A = ab is the original area.
Since αl ≈ 10⁻⁵ K⁻¹, the product αlΔT is very small compared to 2 and can be neglected for practical temperature changes.
Therefore: (ΔA/A)/ΔT ≈ 2αl, proving that the coefficient of area expansion is twice the linear expansivity.
This result, along with αV = 3αl, shows the geometric relationship between the three expansion coefficients for isotropic solids.

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Question 5

Long Form

Compare the specific heat capacities of solids, liquids, and gases as discussed in the chapter. Why does water have the highest specific heat capacity, and what are its practical consequences?

Specific heat capacity s = ΔQ/(mΔT) varies widely among substances; water has the highest value at 4186 J kg⁻¹ K⁻¹, far exceeding metals like copper (386 J kg⁻¹ K⁻¹) or lead (128 J kg⁻¹ K⁻¹).
For gases, two values are defined: Cp at constant pressure and Cv at constant volume; Cp > Cv because at constant pressure the gas does additional work against external pressure during expansion.
Water's exceptionally high specific heat means it requires much more energy to raise its temperature compared to an equal mass of land or metal.
Consequence 1: water warms up more slowly than land during summer and cools more slowly at night, causing sea breezes during the day and land breezes at night.
Consequence 2: water is used as a coolant in automobile radiators because it absorbs large amounts of engine heat without a large temperature rise.
Consequence 3: water is used as a heater in hot water bags because it stores large amounts of heat and releases it slowly, providing sustained warmth.

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Question 6

Long Form

Describe the temperature-time graph obtained when ice at –10°C is slowly heated to form steam at 100°C. Identify all the phases and explain what is happening thermodynamically at each stage.

Stage 1 (–10°C to 0°C): temperature of ice rises steadily as heat is absorbed; the slope depends on the specific heat of ice (2060 J kg⁻¹ K⁻¹).
Stage 2 (at 0°C — melting): temperature remains constant at 0°C while all ice converts to water; heat supplied is used entirely as latent heat of fusion (Lf = 3.33×10⁵ J kg⁻¹) to break intermolecular bonds in ice.
Stage 3 (0°C to 100°C): temperature of water rises steadily; slope is determined by the specific heat of water (4186 J kg⁻¹ K⁻¹), which is smaller slope than ice stage due to higher specific heat.
Stage 4 (at 100°C — vaporisation): temperature remains constant at 100°C while all water converts to steam; heat supplied is used entirely as latent heat of vaporisation (Lv = 22.6×10⁵ J kg⁻¹), much larger than Lf.
Above 100°C: temperature of steam rises again at a rate determined by the specific heat of steam.
The different slopes in each temperature-rising stage reflect the different specific heats of ice, water, and steam; the flat portions reflect the latent heats at 0°C and 100°C.

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Question 7

Long Form

Analyse the mechanism of heat conduction quantitatively. Derive the expression for heat current and explain the significance of thermal conductivity with examples from the chapter.

Conduction is heat transfer through molecular collisions between adjacent parts of a body without any bulk movement of matter; it is most efficient in metals where free electrons also aid heat transfer.
For a bar of length L and cross-section A with ends at temperatures TC and TD (TC > TD), in steady state the heat current H is experimentally found to be: H = KA(TC – TD)/L.
K is the thermal conductivity of the material; its SI unit is J s⁻¹ m⁻¹ K⁻¹ (or W m⁻¹ K⁻¹); a higher K means more rapid heat conduction for the same temperature gradient.
Metals have high K values (silver: 406, copper: 385, aluminium: 205 W m⁻¹ K⁻¹) while insulators have low values (glass wool: 0.04, wood: 0.12, air: 0.024 W m⁻¹ K⁻¹).
Practical application: copper-bottomed cooking pots use copper's high K for uniform heat distribution; plastic foam insulation (which traps air pockets) uses the low K of air to reduce heat loss.
In nuclear reactors, elaborate conduction-based heat transfer systems prevent the reactor core from overheating by rapidly removing the enormous heat generated by fission.

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Question 8

Long Form

Explain convection as a mode of heat transfer. Distinguish between natural and forced convection and analyse how natural convection explains the phenomenon of sea and land breezes.

Convection transfers heat by actual bulk movement of fluid matter (liquid or gas); it differs from conduction in that matter itself moves carrying thermal energy from one region to another.
Natural convection: when a fluid is heated from below, the hot part becomes less dense (expands), rises due to buoyancy, and is replaced by cooler, denser fluid from above; this cycle continues without any external pump.
Forced convection: an external mechanical device (pump, fan, heart) forces the fluid to move; examples include home forced-air heating, automobile cooling systems, and blood circulation in the human body.
Sea breeze (daytime): land heats up faster than water (water has higher specific heat and mixing disperses heat); warm air over land rises, cooler air from sea moves in, creating a sea breeze.
Land breeze (night): at night, land cools faster than water; water surface becomes warmer; air over water rises and cooler air from land moves toward the sea, reversing the cycle.
The human heart acts as the pump in forced convection through the circulatory system, maintaining a uniform body temperature by distributing heat throughout the body.

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Question 9

Long Form

Discuss blackbody radiation, Wien's Displacement Law, and the Stefan-Boltzmann law. Explain how these laws are used to estimate the surface temperature of celestial bodies.

All bodies emit thermal radiation by virtue of their temperature; a blackbody is a perfect absorber and emitter, absorbing all incident radiation and emitting maximally at all wavelengths.
Blackbody radiation has a continuous spectrum; the energy distribution with wavelength at a given temperature shows a characteristic curve with a peak at wavelength λm.
Wien's Displacement Law: λmT = 2.9×10⁻³ m K; as T increases, λm shifts to shorter wavelengths — explaining why iron glows red, then yellow, then white as it is heated.
Stefan-Boltzmann Law: H = AσT⁴ for a perfect blackbody, where σ = 5.67×10⁻⁸ W m⁻² K⁻⁴; for a body with emissivity e, H = AeσT⁴.
Application to celestial bodies: light from the Moon has maximum intensity at λm ≈ 14 μm; using Wien's law, surface temperature of Moon ≈ 200 K. Solar radiation peaks at λm = 4753 Å, giving surface temperature of Sun ≈ 6060 K.
The universality of blackbody radiation curves (depending only on temperature, not size, shape, or material) is a fundamental feature that historically spurred the development of quantum mechanics.

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Hard

Question 10

Long Form

Derive the mathematical expression for Newton's Law of Cooling. Explain how this law can be experimentally verified, and describe the nature of the graph obtained during verification.

Newton's Law of Cooling states that the rate of heat loss is proportional to the excess temperature over surroundings: –dQ/dt = k(T₂ – T₁), where k depends on surface area and nature.
For a body of mass m and specific heat s at temperature T₂, if temperature falls by dT₂ in time dt: dQ = ms·dT₂, so rate of heat loss = ms·(dT₂/dt).
Combining: ms(dT₂/dt) = –k(T₂ – T₁), giving dT₂/(T₂ – T₁) = –(k/ms)dt = –K·dt.
Integrating: log_e(T₂ – T₁) = –Kt + c, or T₂ = T₁ + C′e⁻Kt, showing exponential decay of excess temperature with time.
Experimental verification: a copper calorimeter with hot water is placed in a double-walled vessel; temperature is noted every minute; a graph of log_e(T₂ – T₁) vs time (t) is plotted.
The graph is a straight line with a negative slope, confirming the exponential cooling relationship and validating the law.

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Chapter 10: Thermal Properties of Matter | Long Questions

Describe the construction and working of a constant-volume gas thermometer. How does it establish the concept of absolute temperature, and what is the significance of –273.15°C?

Derive the relation αV = 3αl for an isotropic solid. Hence explain what happens when the thermal expansion of a steel rail is completely prevented, calculating the thermal stress for a 10°C rise.

Explain the anomalous expansion of water between 0°C and 4°C. Discuss its environmental consequences for aquatic life and illustrate using the density-temperature graph described in the chapter.

Derive an expression for the coefficient of area expansion of a rectangular solid in terms of its linear expansivity. Show that the coefficient of area expansion is approximately twice the linear expansivity.

Compare the specific heat capacities of solids, liquids, and gases as discussed in the chapter. Why does water have the highest specific heat capacity, and what are its practical consequences?

Describe the temperature-time graph obtained when ice at –10°C is slowly heated to form steam at 100°C. Identify all the phases and explain what is happening thermodynamically at each stage.

Analyse the mechanism of heat conduction quantitatively. Derive the expression for heat current and explain the significance of thermal conductivity with examples from the chapter.

Explain convection as a mode of heat transfer. Distinguish between natural and forced convection and analyse how natural convection explains the phenomenon of sea and land breezes.

Discuss blackbody radiation, Wien's Displacement Law, and the Stefan-Boltzmann law. Explain how these laws are used to estimate the surface temperature of celestial bodies.

Derive the mathematical expression for Newton's Law of Cooling. Explain how this law can be experimentally verified, and describe the nature of the graph obtained during verification.

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