• Temperature is measure that how body is hot or cold.
  • The SI unit of temperature is Kelvin (K) and Celsius (°C) is commonly used as unit of temperature.
  • If temperature is high, hot environment where temperature is low (or negative), have cold environment.
  • Heat- It is a formed of energy that transfer between 2 or more system and its surrounding due to difference in temperature.
  • The SI unit of heat is Joule (J).
  • The measurement of temperature is by using thermometer and the liquid in thermometer is commonly mercury, alcohol, etc.
  • The thermometer measure in numerically because it is calibrated.
  • The temperature which water starting to freeze is 0°, and on 100° temperature is boiling temperature of water.
  • Temperature also measure in fahrenheit (°F), Celsius (°C) and Kelvin (K).
    • °F = 9/5(°C+32).
    • °C = 5/9(°F-32).
    • K= °C – 273.15.
  • The relationship between °F and °C is –
    • (tF – 32)/180 = tC /100

1. Ideal-Gas Equation and Absolute Temperature

  1. Liquid vs. Gas Thermometers:
    • Liquid thermometers differ in readings due to different expansion properties.
    • Gas thermometers provide consistent readings regardless of gas type because all low-density gases expand similarly.
  2. Basic Gas Laws:
    • Boyle’s Law: At constant temperature, pressure (P) and volume (V) of a gas are inversely proportional: PV=constantPV.
    • Charles’ Law: At constant pressure, the volume (V) of a gas is directly proportional to its temperature (T): V/T=constant.
  3. Ideal-Gas Law:
    • Combining both laws gives PV/T=constant, or PV=μRT, where:
      • μ = Number of moles of gas.
      • R = Universal gas constant = 8.31 J/mol.
    • This law applies to low-density gases under ideal conditions.
  4. Kelvin Temperature Scale:
    • Absolute temperature scale starts at −273.15∘C-273.15^\circ \text{C}−273.15∘C, called absolute zero (0 K).
    • Relationship between Kelvin and Celsius: T=t+273.15, where t is temperature in Celsius.
  5. Real Gases vs. Ideal Gases:
    • Real gases deviate from the ideal-gas law at low temperatures but follow it closely at higher temperatures.

Thermal Expansion

  1. Basic Concept:
    • Most materials expand when heated and contract when cooled.
    • Types:
      • Linear Expansion: Change in length.
      • Area Expansion: Change in surface area.
      • Volume Expansion: Change in volume.
  2. Key Equations:
    • Linear Expansion: Δl/l= αlΔT, where:
      • αl​ = Coefficient of linear expansion.
    • Volume Expansion: ΔV/V=αVΔT, where:
      • αV= Coefficient of volume expansion.
    • Relation: αV=3αl​ (for isotropic materials).
  3. Material Behavior:
    • Metals expand more than glass.
    • Thermal expansion values differ for solids, liquids, and gases (e.g., ethanol expands more than mercury).
  4. Anomalous Behavior of Water:
    • Water contracts on heating from 0C to 4C, then expands beyond 4C.
    • Maximum density at 4C, crucial for aquatic life.
  5. Applications:
    • Hot water loosens metal lids by thermal expansion.
    • Balloon expansion/contraction demonstrates gas behavior.

3. Specific Heat Capacity

  1. Definition:
    • Specific Heat Capacity (s): Heat required to raise the temperature of 1 kg of a substance by 1C.
    • Formula: s= ΔQ​/mΔt, where:
      • ΔQ= Heat absorbed/released.
      • m= Mass.
      • ΔT= Change in temperature.
  2. Molar Specific Heat Capacity (C):
    • Heat capacity per mole of a substance: C= ΔQ​/μΔT​, where μ= Number of moles.
  3. Behavior of Substances:
    • Water has the highest specific heat, making it useful for cooling systems and stabilizing temperatures in nature.
    • Metals heat/cool faster than water due to lower specific heat.
  4. Specific Heat of Gases:
    • At Constant Pressure (Cp​): Heat capacity when pressure is constant.
    • At Constant Volume (Cv​): Heat capacity when volume is constant.
  5. Applications:
    • High specific heat of water explains sea breezes, slow warming of oceans, and its use in radiators and hot water bags.

Extra Knowledge for Competitive Exams

  1. Derived Formulas:
    • PV∝T: Relates gas behavior with temperature.
    • αV=3αl: Useful in problems involving isotropic materials.
  2. Kelvin and Celsius:
    • Understand temperature conversions: T(K)=t(C)+273.15
  3. Thermal Stress:
    • Preventing expansion (e.g., fixing a rod’s ends) creates thermal stress: σ=YαlΔT, where Y= Young’s modulus.
  4. Water’s Anomalous Behavior:
    • Crucial for biology and environmental questions (e.g., lakes freezing top-down).
  5. Gases:
    • Real gases deviate from ideal behavior under high pressure/low temperature due to intermolecular forces.

Calorimetry Basics

  1. Isolated System: A system where no heat is exchanged with surroundings. Heat transfers only within the system:
    • Heat flows from a hotter to a colder part until temperatures equalize.
    • Heat lost by the hot part = Heat gained by the cold part.
  2. Calorimetry: The science of measuring heat:
    • A calorimeter is the device used for measurement.
    • It has a metallic vessel (copper/aluminum) and a stirrer, all enclosed in an insulating jacket to minimize heat loss.
    • A thermometer measures the temperature changes inside the calorimeter.

Key Principle:

In an isolated setup:

  • Heat lost by the hot body = Heat gained by the cold body.
    This principle helps calculate specific heat capacity.

Worked Example: Finding Specific Heat Capacity of Aluminium

  • An aluminium sphere (0.047 kg) heated to 100 °C is placed in water at 20 °C. Final temp = 23 °C.
  • Using the heat transfer formula:
    • Heat lost by sphere = Heat gained by water + Heat gained by calorimeter.
    • Result: Specific heat capacity of aluminium = 0.911 kJ/kg·K.

Change of State

  1. States of Matter: Solid, Liquid, Gas.
    Phase change: Transition between these states (e.g., melting, vaporization).
  2. Key Observations:
    • During a phase change, temperature remains constant.
    • Heat is used to change the state (not to increase temperature).
  3. Important Terms:
    • Melting Point: Temperature at which solid turns to liquid (e.g., Ice → Water at 0 °C).
    • Boiling Point: Temperature at which liquid turns to gas (e.g., Water → Steam at 100 °C at 1 atm).
    • Sublimation: Direct solid-to-gas change (e.g., Dry ice → CO₂ gas).
  4. Pressure Effect:
    • Boiling point increases with pressure (e.g., in pressure cookers).
    • Boiling point decreases at high altitudes (e.g., on mountains).

Latent Heat

  • Definition: Heat required for a phase change without temperature change.
    • Latent Heat of Fusion (Lf): Heat for solid ↔ liquid transition.
    • Latent Heat of Vaporization (Lv): Heat for liquid ↔ gas transition.
  • Formula:Q=m⋅L, Where Q= Heat, m= Mass, L= Latent Heat.
  • Values for Water:
    • LfLfLf (ice to water) = 3.33 × 10⁵ J/kg.
    • LvLvLv (water to steam) = 22.6 × 10⁵ J/kg.

Special Concepts

  1. Triple Point: The temperature and pressure where solid, liquid, and gas phases coexist.
    • For water: 273.16 K, 6.11×10-3 Pa.
  2. Regelation: Ice melts under pressure and refreezes when pressure is relieved.
    • Example: Wire cutting through ice.

Advanced Application

Heat Required to Convert Ice to Steam (Detailed Example):

  • Ice (−12°C) → Water (0°C) → Steam (100°C):
    • Heat for warming ice (Q1).
    • Heat for melting ice (Q2​).
    • Heat for warming water (Q3​).
    • Heat for vaporizing water (Q4​).
    • Total Heat Q= Q1+Q2+Q3+Q4​.

Quick Problem-Solving Tips

  1. Always ensure conservation of energy: Heat lost = Heat gained.
  2. Identify the type of heat transfer:
    • Sensible Heat: Temperature change (Q= m*s*ΔT).
    • Latent Heat: Phase change (Q=m*L).
  3. Account for insulation to minimize errors in competitive exams.

Heat Transfer

  • Heat is energy that transfers due to a temperature difference.
  • There are three modes of heat transfer:
    1. Conduction: Transfer within a material or between touching objects.
    2. Convection: Transfer by the motion of fluids (liquids or gases).
    3. Radiation: Transfer through electromagnetic waves, requiring no medium.

1. Conduction

  • Definition: Heat transfer occurs when energy moves through a material without the material itself moving.
    • Example: A metallic rod heated at one end transfers heat to the other end.
  • Mechanism: Molecules vibrate and pass energy to neighboring molecules.
  • Good Conductors vs. Insulators:
    • Metals like silver, copper, and aluminum are good conductors.
    • Materials like wood, glass wool, and air are poor conductors (insulators).
  • Quantitative Expression:
    • Heat current, H = K A(TC+TD)/L​, where:
      • K: Thermal conductivity (measures a material’s ability to conduct heat).
      • A: Cross-sectional area.
      • L: Length of the material.
      • TC+TD​: Temperatures at two ends.
    • Unit of Thermal Conductivity: W m−1K−1.
    • Higher K: Better conductor.
  • Applications:
    • Copper-bottomed cooking pots for even heat distribution.
    • Thermal insulation in buildings using foam or earth layers to reduce heat flow.
  • Important Note: Gases are poor conductors due to widely spaced molecules.

Example: Calculating the junction temperature in a system with different materials involves setting equal heat currents for both materials. This uses thermal conductivity and geometric parameters.

  • Applications:
    • Copper-bottomed cooking pots for even heat distribution.
    • Thermal insulation in buildings using foam or earth layers to reduce heat flow.
  • Important Note: Gases are poor conductors due to widely spaced molecules.

Example: Calculating the junction temperature in a system with different materials involves setting equal heat currents for both materials. This uses thermal conductivity and geometric parameters.


2. Convection

  • Definition: Heat transfer through bulk movement of fluid particles.
    • Possible only in liquids and gases.
  • Types of Convection:
    1. Natural Convection: Driven by buoyancy (density differences due to temperature).
      • Example: Sea breeze during the day and land breeze at night.
      • Explanation: Warm air rises, cool air replaces it, forming convection currents.
    2. Forced Convection: Fluid is forced to move using a pump or external mechanism.
      • Examples:
        • Car radiator cooling systems.
        • Blood circulation in the human body.
  • Applications:
    • Trade winds: Warm equatorial air rises and moves towards poles; rotation of Earth modifies these patterns.
    • Cooking and heating systems: Faster and uniform heat transfer.

3. Radiation

  • Definition: Heat transfer through electromagnetic waves, requiring no medium.
    • Example: Heat from the Sun reaches Earth through space.
  • Characteristics:
    • All objects emit thermal radiation based on their temperature.
    • Heat transfer happens even in a vacuum.
  • Factors Affecting Radiation:
    • Surface color: Black surfaces absorb and emit more radiation than lighter ones.
    • Example: Black cooking pots absorb maximum heat.
  • Applications:
    • Clothing:
      • Light-colored clothes for summer (reflect sunlight).
      • Dark-colored clothes for winter (absorb heat).
    • Thermos flasks:
      • Reduce heat loss by combining insulation (to prevent conduction), vacuum (to block convection), and reflective surfaces (to minimize radiation).

Key Concepts for Competitive Exams

  1. Conduction Formula:
    Heat flow rate H=K (AΔT)/L.
  2. Thermal Conductivity Comparisons: Metals have high K, while gases and foams have low K.
    • Silver: Best conductor (K=406 W/mK).
    • Air: Poor conductor (K=0.024 W/mK).
  3. Steady State: In conduction, heat flow remains constant at all cross-sections in a steady state.
  4. Convection Currents: Natural convection is driven by buoyancy, and forced convection uses external forces.
  5. Radiation:
    • No medium required.
    • Depends on surface properties (color, texture).

Extra Tips for Exams

  • Units and Dimensions: Always check the units of thermal conductivity, heat current, and related terms.
  • Real-life Examples: Relating theory to daily life (e.g., sea breeze, insulation) makes understanding easier.
  • Quick Tricks:
    • Metals = Good conductors.
    • Insulators = Low K.
    • Radiation = Vacuum and surface-dependent.

1. Blackbody Radiation

  • Definition: Blackbody radiation refers to the thermal radiation emitted by an idealized object that absorbs and emits all radiation incident upon it.
  • Key Properties:
    • Continuous spectrum: The radiation consists of a range of wavelengths.
    • Energy distribution: Varies with wavelength and temperature.
    • Wien’s Displacement Law: The wavelength (λm​) corresponding to maximum energy decreases as temperature (T) increases.
      • λm​T=constant≈2.9×10-3 m\cdotpK.
      • Example: Hot iron changes color with increasing temperature, from dull red to white-hot.
    • Universality: Blackbody curves depend only on temperature, not the size, shape, or material.
  • Applications:
    • Surface temperatures of celestial bodies can be estimated.
    • For instance:
      • Moon’s temperature: T=200 KT (λm=14 μm).
      • Sun’s surface temperature: T=6060 KT (λm=4753 A˚).

2. Stefan-Boltzmann Law

  • Total Radiated Energy:
    • Perfect radiators (emissivity e=1): H=AσT4, where:
      • H: Power radiated (W),
      • A: Surface area (m2),
      • σ=5.67×10-8 W/m2 K4: Stefan-Boltzmann constant,
      • T: Absolute temperature (K).
    • For real objects: H=eAσT4, with e≤1.
  • Net Heat Exchange:
    • H=eσA(T4−T4s), where Ts​ is the surrounding temperature.

3. Heat Loss from Human Body:

  • Example:
    • Skin temperature: 28 C2(~301 K),
    • Room temperature: 22 C(~295 K),
    • Surface area: 1.9 m2,
    • Emissivity (e) of skin: ~0.97.
    • Heat loss rate: H≈66.4 W.
  • Practical Insight: Modern clothing, like those used in Arctic conditions, includes reflective metallic layers to minimize radiative heat loss.

4. Newton’s Law of Cooling

  • Observation: Hot objects cool faster initially, with the rate of cooling slowing as the object approaches room temperature.
  • Mathematical Formulation:
    • −dQ​/dt = k(T−Ts​), where T is the object’s temperature and ​Ts is the surroundings’ temperature.
    • For small temperature differences, ΔT:
      • T−Ts decays exponentially: T= Ts​+Ce−Kt.
  • Applications:
    • Used to estimate cooling times for hot objects like food, drinks, or industrial processes.
    • Example: A pan cooling from 94 C to 86 C takes 2 minutes. From this, the time to cool from 71 C to 69 C can be estimated.

5. Key Thermal Properties and Definitions

  1. Temperature Scales:
    • Kelvin (K): Absolute scale, with T(K)=T(C)+273.15.
    • Celsius and Fahrenheit related byF= 9/5 C+32.
  2. Thermal Expansion:
    • Linear expansion: Δl/l=αl​ΔT..
    • Volume expansion: ΔV/V= αvΔT.
    • Relation: αv​=3αl​.
  3. Heat Capacity:
    • Specific heat: s=ΔQ/(mΔT).
    • Molar heat: C=ΔQ/(μΔT).
  4. Latent Heat:
    • Heat required for phase changes:
      • Fusion (Lf​): Solid ↔ Liquid.
      • Vaporization (Lv​): Liquid ↔ Gas.

6. Modes of Heat Transfer

  1. Conduction:
    • Heat flow through solids: H=KA(T1​−T2)/L, where K is thermal conductivity.
  2. Convection:
    • Heat transfer in fluids by movement of particles.
  3. Radiation:
    • Heat transfer via electromagnetic waves, effective even in a vacuum.

Practice Questions for Competitive Exams

  1. Conceptual:
    • Why does the color of a blackbody change with temperature? Relate it to Wien’s Law.
  2. Numerical:
    • Calculate the net heat radiated by a body with emissivity 0.8, temperature 500 K, area 0.5m2, and surroundings at 300 K.
  3. Graph-based:
    • Sketch and interpret cooling curves for different surrounding temperatures.
  4. Derivations:
    • Derive T= Ts+CeKt from Newton’s cooling law.