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Thermal Properties of Matter

Ch. 7Std 11

Easy Overview

Why does a metal lid expand when heated, making it easier to open a tight jar? Why does a lake freeze from the top down instead of the bottom up? And why do you feel colder on a breezy 20 degree C day than on a still 20 degree C day? The study of thermal properties of matter answers all these questions. This chapter is about heat - what it is, how it moves, and how it changes the materials around us. We will explore temperature scales, thermal expansion of solids, liquids, and gases, the strange behavior of water near freezing, heat capacity and specific heat, latent heat of phase changes, heat transfer through conduction, convection, and radiation, and Newton's law of cooling. These are not just textbook topics - they are the physics behind how a thermos keeps your coffee hot, why cooking pots have metal bottoms and plastic handles, why deserts get freezing cold at night, and how a pressure cooker cooks food faster.

Temperature and Heat - The Basic Distinction

Temperature and heat are NOT the same thing. Temperature measures how hot or cold something is - it is proportional to the average kinetic energy of the molecules. Heat is energy transferred between objects because of temperature difference. A cup of coffee at 80 degrees C has a higher temperature than a bathtub at 40 degrees C, but the bathtub contains far more heat energy because it has so much more water. Temperature tells you the intensity of thermal motion; heat tells you the total thermal energy content. Heat flows naturally from higher temperature to lower temperature - never the other way. A thermometer measures its own temperature, which reaches equilibrium with the object.

Temperature Scales

Celsius: 0 degrees C = freezing point of water, 100 degrees C = boiling point at standard pressure. Fahrenheit: 32 degrees F = freezing, 212 degrees F = boiling. Kelvin is the SI unit - absolute scale starting at absolute zero (-273.15 degrees C). No negative Kelvin temperatures. Conversion: K = degrees C + 273.15, degrees F = (9/5)degrees C + 32, degrees C = (5/9)(degrees F - 32). The Kelvin scale is fundamental because many formulas (ideal gas law, thermodynamic efficiency) require absolute temperature. At absolute zero (0 K), molecular motion theoretically stops. Room temperature is about 300 K (27 degrees C). The difference between two temperatures is the same in Celsius and Kelvin.

Thermal Expansion - Linear

Most solids expand when heated. Linear expansion: delta L = alpha L_0 delta T, where alpha is the coefficient of linear expansion (unit: per degree C or per K). Different materials expand differently: steel alpha about 11 x 10^-6 /C, aluminum alpha about 23 x 10^-6 /C, glass alpha about 9 x 10^-6 /C. A steel bridge 100 m long on a cold day (10 degrees C) might expand by about 3.3 cm on a hot summer day (40 degrees C). That is why bridges have expansion joints - gaps that allow the bridge to expand and contract. Railway tracks have similar gaps. If expansion is not accommodated, the stress can cause buckling - that is why concrete roads have cut sections filled with flexible material.

Thermal Expansion - Areal and Volume

Area expansion: delta A = beta A_0 delta T, where beta = 2 alpha. Volume expansion: delta V = gamma V_0 delta T, where gamma = 3 alpha for isotropic materials. A steel sheet with alpha = 11 x 10^-6 has beta = 22 x 10^-6 and gamma = 33 x 10^-6 per degree C. For liquids, only volume expansion matters since liquids have no fixed shape. Liquids generally have larger expansion coefficients than solids - that is why a full bottle of liquid left in the freezer might burst. The expansion of liquid in a thermometer is what makes it work. Bi-metallic strips use differential expansion of two metals bonded together - when heated they bend, used in thermostats.

Anomalous Expansion of Water

Most substances expand when heated and contract when cooled. Water is weird: between 0 degrees C and 4 degrees C, water contracts when heated! At 4 degrees C, water has its maximum density (minimum volume). Below 4 degrees C, it expands again, becoming less dense. This is why ice floats - ice at 0 degrees C is less dense (about 917 kg/m^3) than water at 4 degrees C (1000 kg/m^3). The implications are huge: when a lake cools in winter, the surface water reaches 4 degrees C and sinks (because it is denser). Deeper water remains at 4 degrees C while the surface cools further and forms ice. The ice layer acts as an insulator, protecting aquatic life below. If water behaved normally, lakes would freeze from the bottom up.

Specific Heat Capacity

Specific heat capacity c is the heat required to raise the temperature of 1 kg of a substance by 1 degree C (or 1 K). Unit: J/(kg-K). Water has an unusually high specific heat: c = 4186 J/(kg-K). That is why coastal areas have moderate climates - water heats up and cools down slowly. Sand has low specific heat (~800 J/(kg-K)), so it heats up quickly during the day and cools quickly at night. Heat capacity C = mc. Heat required: Q = mc delta T = C delta T. To heat 2 kg of water from 20 to 100 degrees C: Q = 2 x 4186 x 80 = 669,760 J. This is why it takes time to boil water.

Latent Heat - Phase Changes

Latent heat L is the heat absorbed or released during a phase change at constant temperature. No temperature rise occurs during melting, boiling, or condensation - all the energy goes into changing the phase. Latent heat of fusion L_f: heat to melt ice at 0 degrees C to water at 0 degrees C = 334 kJ/kg. Latent heat of vaporization L_v: heat to boil water at 100 degrees C to steam at 100 degrees C = 2260 kJ/kg. L_v is much larger than L_f - breaking all intermolecular bonds to turn liquid into gas takes way more energy. That is why steam burns are so dangerous - steam releases its latent heat when it condenses on your skin. Water's high latent heat of vaporization is why sweating cools you.

Calorimetry - Measuring Heat Transfer

Calorimetry is about measuring heat transfer. The principle: heat lost by hot bodies = heat gained by cold bodies (in an isolated system). A calorimeter is a metal container with a stirrer and thermometer, insulated from surroundings. To find specific heat: heat the substance to a known temperature, drop it into the calorimeter containing water, measure the final equilibrium temperature. The heat lost by the substance equals the heat gained by water plus calorimeter: m_1 c_1 (T_1 - T_f) = m_2 c_2 (T_f - T_2) + m_cal c_cal (T_f - T_2). The water equivalent of a calorimeter is the mass of water that would absorb the same heat as the calorimeter. Do not forget the calorimeter itself absorbs heat too.

Heat Transfer - Conduction

Conduction is heat transfer through a material without the material itself moving. Heat flows from the hot end to the cold end. Fourier's law: rate of heat flow H = -kA(dT/dx), where k is thermal conductivity (W/m-K), A is cross-section area, dT/dx is temperature gradient. For a uniform rod: H = kA(T_1 - T_2)/L. Metals have high k (copper: 400 W/m-K, aluminum: 237 W/m-K) - cooking pots have metal bases. Wood and plastics have very low k (~0.1 W/m-K) - saucepan handles are plastic. Air is a terrible conductor (~0.02 W/m-K) - double-pane windows with air gaps insulate well.

Heat Transfer - Convection and Radiation

Convection is heat transfer by fluid movement. As a fluid is heated, it expands, becomes less dense, and rises. Cooler fluid moves in to replace it, creating a convection current. Natural convection: the wind on a beach (land heats faster, warm air rises, cool sea air moves in). Forced convection: a fan blowing air over a hot surface. Radiation is heat transfer via electromagnetic waves (infrared) - no medium needed. The Stefan-Boltzmann law: power radiated P = epsilon sigma A T^4, where sigma = 5.67 x 10^-8 W/m^2-K^4, epsilon is emissivity (0 to 1). A blackbody has epsilon = 1. Dark rough surfaces are good emitters/absorbers. Shiny surfaces are poor emitters/absorbers - thermos flasks use silvered surfaces to reflect radiation.

Newton's Law of Cooling

Newton's law of cooling: the rate of heat loss by a body is proportional to the temperature difference between the body and its surroundings: dT/dt = -k(T - T_s). This holds for relatively small temperature differences (up to about 30 degrees C). The solution is T = T_s + (T_0 - T_s)e^(-kt). The body cools quickly at first, then more slowly as it approaches surroundings temperature. Experimentally, plot ln(T - T_s) vs t - a straight line with slope -k. The cooling constant k depends on surface area, nature of surface, and surrounding medium. Applications: estimating cooling time of hot beverages, designing cooling systems, forensics (estimating time of death from body temperature). Valid only for small temperature differences.

Key Points

  • •Temperature: measure of average KE of molecules. Heat: energy transferred due to temperature difference.
  • •Absolute zero = -273.15 C = 0 K. K = C + 273.15. No negative Kelvin.
  • •Linear expansion: delta L = alpha L_0 delta T. Expansion joints in bridges and rails.
  • •Area expansion: beta = 2 alpha. Volume expansion: gamma = 3 alpha for isotropic solids.
  • •Anomalous expansion of water: density maximum at 4 C. Ice less dense than water.
  • •Specific heat c: heat to raise 1 kg by 1 C. Q = mc delta T. Water: c = 4186 J/(kg-K).
  • •Latent heat of fusion L_f = 334 kJ/kg. Latent heat of vaporization L_v = 2260 kJ/kg.
  • •Calorimetry principle: heat lost = heat gained (isolated system).
  • •Conduction: H = kA(delta T/L). Metals high k, insulators low k.
  • •Convection: heat transfer by fluid movement. Natural and forced.
  • •Radiation: P = epsilon sigma A T^4. sigma = 5.67 x 10^-8 W/m^2-K^4.
  • •Newton's cooling: dT/dt = -k(T - T_s). Exponential decay to surroundings temperature.
  • •Emissivity epsilon: 1 for blackbody, 0 for perfect reflector. Dark surfaces high epsilon.
  • •Phase changes occur at constant temperature with latent heat.

Practice Questions

  • Define specific heat and latent heat. 500 g ice at 0 C mixed with 500 g water at 80 C. Find final temperature. (L_f = 334 kJ/kg, c = 4186 J/(kg-K))
  • A metal rod of length 1 m at 20 C expands by 0.55 mm when heated to 120 C. Find alpha and length at 0 C.
  • State Newton's law of cooling. A body cools from 80 to 60 C in 5 min. Surroundings at 30 C. Find time to cool from 60 to 40 C.
  • Derive expression for rate of heat conduction through a composite wall of two materials.
  • Explain anomalous expansion of water. Why does ice float? Why do lakes freeze from top?
  • Describe how to determine specific heat of a solid using the method of mixtures.
  • A copper sphere of radius 5 cm at 200 C in a room at 20 C. sigma = 5.67 x 10^-8, epsilon = 0.8. Find initial rate of heat loss by radiation.
  • Distinguish between conduction, convection, and radiation with two daily-life examples each.