THERMAL PROPERTIES OF MATTER-QnA

Q1: What is temperature?

Temperature is a physical quantity that indicates the degree of hotness or coldness of a body and determines the direction of heat flow between bodies in contact.

Q2: Name the SI unit of heat.

The SI unit of heat is joule (J).

Q3: What is thermal equilibrium?

Thermal equilibrium is the state in which two bodies in contact have the same temperature and no net heat transfer occurs between them.

Q4: Define specific heat capacity.

Specific heat capacity is the amount of heat required to raise the temperature of unit mass of a substance by one kelvin.

Q5: What is linear expansion?

Linear expansion is the increase in length of a solid when its temperature is increased.

Q6: State the unit of coefficient of linear expansion.

The unit of coefficient of linear expansion is K?¹.

Q7: What is calorimetry?

Calorimetry is the experimental method used to measure the amount of heat exchanged during thermal processes.

Q8: What is latent heat?

Latent heat is the heat absorbed or released by a substance during a change of state without any change in temperature.

Q9: Name the mode of heat transfer that does not require a medium.

Radiation is the mode of heat transfer that does not require a material medium.

Q10: What is a black body?

A black body is an ideal body that absorbs all incident radiation and emits the maximum possible radiation at a given temperature.

Q11: Define emissivity.

Emissivity is the ratio of radiation emitted by a surface to that emitted by a perfect black body at the same temperature.

Q12: What is the principle of thermometer?

A thermometer works on the principle that some physical property of a substance changes uniformly with temperature.

Q13: What is thermal conductivity?

Thermal conductivity is the ability of a material to conduct heat through it.

Q14: What is Newton’s law of cooling?

Newton’s law of cooling states that the rate of loss of heat of a body is proportional to the difference between its temperature and that of its surroundings.

Q15: What is absolute zero?

Absolute zero is the lowest possible temperature at which molecular motion is minimum and no further cooling is possible.

Q1: Distinguish between heat and temperature.

Heat is energy in transit due to temperature difference, while temperature is a measure of thermal state of a body. Heat depends on mass; temperature does not.

Q2: Why is mercury preferred in thermometers?

Mercury expands uniformly, does not wet glass, has a wide temperature range, and provides clear visibility, making it suitable for precise temperature measurement.

Q3: Define coefficient of volume expansion.

It is the fractional change in volume of a substance per unit rise in temperature.

Q4: What is anomalous expansion of water?

Between 0 °C and 4 °C, water contracts on heating and expands on cooling, unlike most substances; this behavior is called anomalous expansion.

Q5: Why do railway tracks have gaps?

Gaps are provided to allow thermal expansion of rails during hot weather, preventing bending or buckling.

Q6: State Fourier’s law of heat conduction.

Fourier’s law states that the rate of heat flow through a material is proportional to the temperature gradient and cross-sectional area.

Q7: What factors affect the rate of heat conduction?

Rate of heat conduction depends on thermal conductivity, temperature difference, cross-sectional area, and length of the conductor.

Q8: Why does metal feel colder than wood at the same temperature?

Metal conducts heat faster than wood, so it draws heat from the body more rapidly, giving a colder sensation.

Q9: What is Stefan–Boltzmann law?

It states that the radiant energy emitted per unit area of a black body is proportional to the fourth power of its absolute temperature.

Q10: Define thermal stress.

Thermal stress is the stress developed in a body when its expansion or contraction due to temperature change is restricted.

Q1: Explain linear, areal, and volume expansion.

Linear expansion refers to change in length, areal expansion to change in surface area, and volume expansion to change in volume of a substance due to temperature rise.

Q2: Derive the relation between coefficients of expansion.

For isotropic solids, the coefficient of area expansion is approximately twice the coefficient of linear expansion, and the coefficient of volume expansion is approximately three times the linear coefficient, assuming small temperature changes.

Q3: Explain heat transfer by conduction.

Conduction is the transfer of heat through a material without actual movement of particles, occurring due to temperature gradients within the substance.

Q4: Describe convection with an example.

Convection involves heat transfer through the bulk motion of fluid particles. For example, warm air rising above a heater demonstrates natural convection.

Q5: Explain radiation as a mode of heat transfer.

Radiation transfers heat in the form of electromagnetic waves and does not require a medium, allowing energy transfer through vacuum.

Q1: Explain the concept of specific heat capacity and its significance.

Specific heat capacity represents a fundamental thermal property measuring the heat energy needed to raise the temperature of unit mass of a substance by one degree. This property reveals how different materials respond to heat addition, with profound implications for everyday thermal processes and engineering designs [web:31][web:32].

Definition
The specific heat capacity \( c \) denotes the heat required to increase the temperature of 1 kg of substance by 1 K (or 1°C).
Mathematically expressed as \[ c = \frac{Q}{m \Delta T} \] where \( Q \) signifies heat supplied in joules, \( m \) the mass in kilograms, and \( \Delta T \) the temperature rise in kelvin or °C [web:31][web:32].

SI Unit
The standard unit stands as \[ \mathrm{J\, kg^{-1} K^{-1}} \] reflecting energy per unit mass per degree temperature change [web:32][web:33].

Physical Meaning
Specific heat capacity gauges a material's resistance to temperature variation: substances possessing high values demand substantial heat for modest temperature gains, whereas low values permit rapid heating. Water exemplifies high specific heat capacity at approximately 4180 J kg\(^{-1}\) K\(^{-1}\), enabling effective climate moderation and coolant roles in engines [web:31][web:36].

Heat Transfer Relation
Heat exchanged during temperature change \( \Delta T \) for mass \( m \) follows \[ Q = m c \Delta T \] providing the cornerstone for calorimetry computations [web:32].

Importance and Applications
This property elucidates moderate coastal climates through water's thermal inertia, guides calorimetry experiments for unknown properties, informs heating-cooling system designs, and facilitates material thermal behavior comparisons [web:36][web:40]. Engineers leverage it in radiators, storage heaters, and insulation selections ensuring optimal energy management [web:40].

Q2: Describe the principle, construction, and working of a constant volume gas thermometer.

A constant volume gas thermometer operates on the principle that pressure of a fixed volume of gas is directly proportional to its absolute temperature when volume remains constant. This relationship, expressed as \( P \propto T \) or \( \frac{P}{T} = \) constant, forms the foundation of absolute temperature measurement with high precision across wide ranges.

Construction consists of a gas bulb connected to a mercury manometer through a narrow capillary tube. The bulb, typically made of thin glass or quartz, contains a fixed quantity of inert gas like helium or hydrogen at low pressure. The capillary tube ensures volume constancy during temperature changes as the gas expands only within its fixed length. Pressure measurement occurs via a U-shaped mercury manometer where one limb connects to the capillary while the other remains open to atmosphere, displaying pressure difference directly.

Working begins with calibration at known temperatures. At the ice point (273.15 K), initial pressure reads \( P_0 \). At steam point (373.15 K), pressure becomes \( P_{100} \). The thermometer temperature \( T \) for any unknown temperature follows: $$\begin{aligned} \frac{P}{P_0} &= \frac{T}{273.15} \\ T &= 273.15 \times \frac{P}{P_0} \end{aligned}$$ For practical use between ice and steam points: $$\begin{aligned} T &= 273.15 + 100 \times \frac{P - P_0}{P_{100} - P_0} \end{aligned}$$ During measurement, the bulb immersion in the substance under test causes gas pressure change, read directly from manometer height difference. Volume remains constant as mercury meniscus stays fixed at a reference mark on the capillary through slight level adjustments. This design achieves exceptional accuracy since gas pressure-temperature linearity holds ideally for rarefied gases, defining the thermodynamic temperature scale with minimal corrections for real gas deviations at low pressures.

Q3: Explain Newton’s law of cooling and its limitations.

Newton's law of cooling states that the rate of heat loss by a body is directly proportional to the temperature difference between the body and its surroundings. Mathematically, this appears as the differential equation \(\frac{dT}{dt} = -k(T - T_s)\), where \(T\) represents the body's temperature at time \(t\), \(T_s\) denotes the surrounding temperature, and \(k\) serves as the positive cooling constant depending on surface area, emissivity, and air circulation.

Solving this separable differential equation yields the temperature-time relation: $$\begin{aligned} \frac{dT}{T - T_s} &= -k\, dt \\ \int_{T_0}^{T} \frac{dT'}{T' - T_s} &= -k \int_0^t dt' \\ \ln\left(\frac{T - T_s}{T_0 - T_s}\right) &= -kt \\ T(t) &= T_s + (T_0 - T_s)e^{-kt} \end{aligned}$$ Here \(T_0\) marks the initial temperature. The exponential decay shows temperature approaching surroundings asymptotically, with cooling fastest when the initial difference proves largest.

The law finds practical verification through experiments where hot objects cool faster in colder environments. For small temperature differences relative to surroundings, an approximate linear relation emerges: \(\frac{\Delta T}{\Delta t} \approx -k(\langle T \rangle - T_s)\), using average temperature \(\langle T \rangle\) during interval \(\Delta t\).

Despite utility, significant limitations exist. The law assumes perfect convection-dominated heat transfer, neglecting radiation dominant at high temperatures (above ~100°C) where Stefan's law prevails. It requires laminar airflow, failing amid turbulence or strong natural convection currents. Very small temperature differences trigger conduction dominance over convection. Finally, the model presumes constant \(k\), unrealistic when emissivity varies or surface conditions change during cooling. These constraints limit accuracy to moderate temperature differences (typically 10-50°C) under controlled convective conditions, explaining discrepancies in kitchen cooling experiments versus theoretical predictions.

Q4: Discuss thermal expansion of solids and its practical applications.

Thermal expansion in solids occurs when heating increases atomic vibrations, causing particles to push apart and enlarge dimensions. This fundamental phenomenon manifests as linear, superficial, or volume expansion depending on the observable change, with fractional expansions proportional to temperature rise according to \(\Delta L/L = \alpha \Delta T\), where \(\alpha\) represents the coefficient of linear expansion characteristic of each material.

Linear expansion dominates one-dimensional objects like rods or wires, where length change follows \(\Delta L = L_0 \alpha \Delta T\). For thin plates, superficial expansion combines effects in two dimensions: \(\Delta A/A_0 = 2\alpha \Delta T\). Three-dimensional solids exhibit volume expansion \(\Delta V/V_0 = 3\alpha \Delta T\), revealing the isotropic nature of thermal expansion in most polycrystalline materials. Different substances display distinctive \(\alpha\) values—aluminium expands nearly twice as much as steel for identical temperature changes, guiding material selection in engineering.

Practical applications abound across engineering disciplines. Bimetallic strips exploit differential expansion rates between metals like brass and steel, bending predictably when heated to operate thermostats, fire alarms, and circuit breakers. Expansion joints in bridges and railway tracks prevent buckling by accommodating concrete and steel elongation during summer heat. Glass thermometers utilize mercury's expansion within a narrow bore to measure temperature precisely. Cooking utensils feature handles of low-expansion materials like wood or bakelite, remaining cool while metal bodies conduct heat efficiently.

Modern applications extend further. Precision instruments employ Invar alloy with near-zero \(\alpha\) for stable dimensions in telescopes and measuring tapes. Roller bearings in automobile engines incorporate expansion gaps preventing seizure during operation. Power plant turbines use compensated designs accounting for blade elongation under high temperatures. These examples demonstrate how controlled thermal expansion enhances safety, reliability, and functionality across transportation infrastructure, household appliances, and scientific instrumentation, transforming a fundamental physical effect into essential engineering solutions.

Q5: Explain black body radiation and its importance in thermal physics.

Black body radiation represents the thermal electromagnetic radiation emitted by an ideal absorber called a black body, which perfectly absorbs all incident radiation regardless of wavelength or angle. This idealized object maintains thermal equilibrium by emitting radiation with a characteristic continuous spectrum determined solely by its temperature, independent of material composition, shape, or surface structure. Real approximations include a small hole in a heated cavity where radiation undergoes multiple internal reflections ensuring near-complete absorption.

Theoretical significance emerged dramatically through classical physics failure. Rayleigh-Jeans law predicted infinite energy at short wavelengths—the "ultraviolet catastrophe"—contradicting experimental cavity radiation measurements showing peak intensity shifting to shorter wavelengths with rising temperature per Wien's displacement law: \(\lambda_{\max} T = 2898\,\mu\text{m·K}\). Stefan-Boltzmann law quantifies total radiated power: \(\sigma T^4\), while Planck's revolutionary quantum hypothesis resolved the crisis.

Planck postulated energy quantization \(E = nh\nu\), yielding the spectral energy density: $$\begin{aligned} u(\nu,T) &= \frac{8\pi h \nu^3}{c^3} \frac{1}{e^{h\nu/kT}-1} \end{aligned}$$ This distribution matches observations perfectly, birthing quantum mechanics and earning Planck the 1918 Nobel Prize. At long wavelengths, quantum formula recovers Rayleigh-Jeans classical limit; short wavelengths exhibit exponential Wien tail.

Importance permeates thermal physics and astrophysics. Stars approximate black bodies—Sun's 5800 K surface yields peak green-yellow radiation explaining white appearance. Cosmic microwave background radiation at 2.7 K represents cooled Big Bang remnant, precisely following Planck curve. Laboratory applications include precision thermometry via spectral analysis, incandescent lamp efficiency optimization, and furnace temperature measurement through optical pyrometry. Climate models employ black body approximations for planetary energy balance calculations. Modern quantum technologies trace origins to this foundational problem, underscoring black body radiation's pivotal role bridging classical thermodynamics and twentieth-century physics revolutions.