Chapter 10 ยท Introduction

Chapter 10 โ€” Thermal Properties of Matter

Why railway lines have gaps, why a pressure cooker cooks faster, why a copper-bottomed pan heats evenly and why hot tea cools fastest at first: the physics of temperature, heat and how heat moves.

Between a cold winter night and a hot summer afternoon, a steel railway line a kilometre long can grow by about half a metre; engineers leave small gaps, or stretch the rails while laying them, so that the track does not buckle. A lake in a Himalayan winter freezes from the top down, and the fish survive in liquid water at $4\ ^\circ\text{C}$ underneath. A pressure cooker cooks rice at about $120\ ^\circ\text{C}$ although an open pan of water will never get hotter than $100\ ^\circ\text{C}$. And a cup of tea left on the table loses heat quickly at first and then more and more slowly, as if reluctant to reach room temperature.

This chapter explains all of these with a handful of ideas. You will first separate temperature (how hot a body is) from heat (energy that flows because of a temperature difference), build temperature scales and see how the behaviour of gases leads to the absolute (kelvin) scale and the ideal-gas equation $pV=nRT$. Then you will measure how solids, liquids and gases expand when heated โ€” and why water is the famous exception. Next comes the bookkeeping of heat: specific heat capacity, the method of mixtures in a calorimeter, and the latent heat that melts ice or boils water without changing its temperature. Finally you will follow heat on the move by conduction, convection and radiation, and finish with Newton's law of cooling โ€” the reason your tea behaves as it does.

ยฐC, ยฐF, Kโ†’$pV=nRT$โ†’$\Delta L=\alpha L\,\Delta T$โ†’$Q=mc\,\Delta T$โ†’Calorimetryโ†’$Q=mL$โ†’$H=KA\dfrac{\Delta T}{L}$โ†’$\sigma T^4$โ†’Newton's law of cooling
๐ŸŽฏ By the end of this chapter you canโ€ฆ
  • distinguish heat from temperature and convert between the Celsius, Fahrenheit and kelvin scales, including thermometers with arbitrary fixed points;
  • use the ideal-gas equation $pV=nRT$ and explain how a constant-volume gas thermometer defines absolute zero;
  • calculate linear, area and volume expansion with $\Delta L=\alpha L\,\Delta T$, $\beta\approx2\alpha$, $\gamma\approx3\alpha$, and explain the bimetallic strip and the anomalous expansion of water;
  • use $Q=mc\,\Delta T$, heat capacity and molar specific heat capacity, and solve method-of-mixtures problems in a calorimeter;
  • describe changes of state, read a heating curve, and use $Q=mL$ for melting and boiling โ€” including mixtures in which some ice is left unmelted;
  • calculate the rate of conduction $H=KA\dfrac{T_1-T_2}{L}$ through single and compound slabs, and describe convection;
  • use the Stefanโ€“Boltzmann law and Wien's displacement law for thermal radiation;
  • apply Newton's law of cooling, in its average-rate form and as an exponential decay of the temperature excess;
  • tackle Board, JEE Main, JEE Advanced and NEET-style problems on thermal properties of matter.
Teaser โ€” Milk Now or Milk Later?

You pour $200\ \text{g}$ of tea at $90\ ^\circ\text{C}$ in a $25\ ^\circ\text{C}$ room, and you will drink it after a wait you choose. You also have $50\ \text{g}$ of cold milk. Should you add the milk at once or just before drinking? Guess first, then press Play. (Model: the cooling rate is proportional to how far the cup is above room temperature, and smaller for the bigger, fuller cup; milk and tea have the same specific heat capacity.)

10 min
milk at once: drink atโ€”
milk later: drink atโ€”
differenceโ€”

Sections in this chapter

10.1

Temperature, the Ideal-Gas Law and Thermal Expansion

Heat and temperature, the Celsius, Fahrenheit and kelvin scales, the gas thermometer and absolute zero, and how solids, liquids and gases expand.

$\Delta L=\alpha L\,\Delta T$
Open section โ†’10.2

Specific Heat, Calorimetry, Change of State and Latent Heat

How much heat warms a body, the method of mixtures, melting and boiling, the heating curve and latent heat.

$Q=mc\,\Delta T,\ \ Q=mL$
Open section โ†’10.3

Heat Transfer and Newton's Law of Cooling

Conduction through slabs and compound walls, convection, blackbody radiation with Stefan's and Wien's laws, and the cooling curve.

$H=KA\dfrac{T_1-T_2}{L}$
Open section โ†’
โœ… Before you start
You will need energy and its unit, the joule, with work, kinetic and potential energy and power (Class 11 Physics, Section 5.1 and Section 5.3); stress, strain and Young's modulus for thermal stress (Section 8.2); and pressure, atmospheric pressure and the pascal (Chapter 9, Section 9.1). Rates of change written as $\dfrac{dT}{dt}$ come from Chapter 2 (Section 2.1), and every answer obeys the significant-figure rules of Section 1.2. From Class 9โ€“10 Science it helps to remember the three states of matter and that matter is made of moving particles. The mole and Avogadro's number are used in the ideal-gas equation.
โ† 9.4 Surface Tension and Capillarity10.1 Temperature, the Ideal-Gas Law and Thermal Expansion โ†’