TEMPERATURE AND HEAT-
- 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).
MEASUREMENT OF TEMPERATURE-
- 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
IDEAL GAS EQUATION AND ABSOLUTE TEMPERATURE-
1. Ideal-Gas Equation and Absolute Temperature
- 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.
- 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.
- 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.
- Combining both laws gives PV/T=constant, or PV=μRT, where:
- 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.
- 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
- 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.
- 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).
- Linear Expansion: Δl/l= αlΔT, where:
- Material Behavior:
- Metals expand more than glass.
- Thermal expansion values differ for solids, liquids, and gases (e.g., ethanol expands more than mercury).
- Anomalous Behavior of Water:
- Water contracts on heating from 0∘C to 4∘C, then expands beyond 4∘C.
- Maximum density at 4∘C, crucial for aquatic life.
- Applications:
- Hot water loosens metal lids by thermal expansion.
- Balloon expansion/contraction demonstrates gas behavior.
3. Specific Heat Capacity
- Definition:
- Specific Heat Capacity (s): Heat required to raise the temperature of 1 kg of a substance by 1∘C.
- Formula: s= ΔQ/mΔt, where:
- ΔQ= Heat absorbed/released.
- m= Mass.
- ΔT= Change in temperature.
- Molar Specific Heat Capacity (C):
- Heat capacity per mole of a substance: C= ΔQ/μΔT, where μ= Number of moles.
- 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.
- Specific Heat of Gases:
- At Constant Pressure (Cp): Heat capacity when pressure is constant.
- At Constant Volume (Cv): Heat capacity when volume is constant.
- 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
- Derived Formulas:
- PV∝T: Relates gas behavior with temperature.
- αV=3αl: Useful in problems involving isotropic materials.
- Kelvin and Celsius:
- Understand temperature conversions: T(K)=t(C)+273.15
- Thermal Stress:
- Preventing expansion (e.g., fixing a rod’s ends) creates thermal stress: σ=YαlΔT, where Y= Young’s modulus.
- Water’s Anomalous Behavior:
- Crucial for biology and environmental questions (e.g., lakes freezing top-down).
- Gases:
- Real gases deviate from ideal behavior under high pressure/low temperature due to intermolecular forces.
Calorimetry Basics
- 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.
- 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
- States of Matter: Solid, Liquid, Gas.
Phase change: Transition between these states (e.g., melting, vaporization). - Key Observations:
- During a phase change, temperature remains constant.
- Heat is used to change the state (not to increase temperature).
- 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).
- 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
- Triple Point: The temperature and pressure where solid, liquid, and gas phases coexist.
- For water: 273.16 K, 6.11×10-3 Pa.
- 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
- Always ensure conservation of energy: Heat lost = Heat gained.
- Identify the type of heat transfer:
- Sensible Heat: Temperature change (Q= m*s*ΔT).
- Latent Heat: Phase change (Q=m*L).
- 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:
- Conduction: Transfer within a material or between touching objects.
- Convection: Transfer by the motion of fluids (liquids or gases).
- 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.
- Heat current, H = K A(TC+TD)/L, where:
- 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:
- 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.
- Forced Convection: Fluid is forced to move using a pump or external mechanism.
- Examples:
- Car radiator cooling systems.
- Blood circulation in the human body.
- Examples:
- Natural Convection: Driven by buoyancy (density differences due to temperature).
- 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).
- Clothing:
Key Concepts for Competitive Exams
- Conduction Formula:
Heat flow rate H=K (AΔT)/L. - 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).
- Steady State: In conduction, heat flow remains constant at all cross-sections in a steady state.
- Convection Currents: Natural convection is driven by buoyancy, and forced convection uses external forces.
- 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.
- λmT=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.
- Perfect radiators (emissivity e=1): H=AσT4, where:
- 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
- Temperature Scales:
- Kelvin (K): Absolute scale, with T(K)=T(C)+273.15.
- Celsius and Fahrenheit related byF= 9/5 C+32.
- Thermal Expansion:
- Linear expansion: Δl/l=αlΔT..
- Volume expansion: ΔV/V= αvΔT.
- Relation: αv=3αl.
- Heat Capacity:
- Specific heat: s=ΔQ/(mΔT).
- Molar heat: C=ΔQ/(μΔT).
- Latent Heat:
- Heat required for phase changes:
- Fusion (Lf): Solid ↔ Liquid.
- Vaporization (Lv): Liquid ↔ Gas.
- Heat required for phase changes:
6. Modes of Heat Transfer
- Conduction:
- Heat flow through solids: H=KA(T1−T2)/L, where K is thermal conductivity.
- Convection:
- Heat transfer in fluids by movement of particles.
- Radiation:
- Heat transfer via electromagnetic waves, effective even in a vacuum.
Practice Questions for Competitive Exams
- Conceptual:
- Why does the color of a blackbody change with temperature? Relate it to Wien’s Law.
- Numerical:
- Calculate the net heat radiated by a body with emissivity 0.8, temperature 500 K, area 0.5m2, and surroundings at 300 K.
- Graph-based:
- Sketch and interpret cooling curves for different surrounding temperatures.
- Derivations:
- Derive T= Ts+Ce–Kt from Newton’s cooling law.
These all are the notes of chapter 10 in physics. And after some time you get important questions and NCERT solutions HERE. *#THANKS FOR VISITING, VISIT AGAIN#* 😊