Heat: Expansion, Capacity, Gas Laws, Transfer

What you need to know

• Heat is a form of energy measured in joules; temperature is the degree of hotness of a body and determines the direction of heat flow. Heat always flows from a body at higher temperature to one at lower temperature until they reach thermal equilibrium.
• Celsius and kelvin are related by T(K) = theta(C) + 273. Absolute zero is 0 K or -273 degrees Celsius. Fahrenheit converts by F = (9/5)C + 32, and the two scales read the same at -40 degrees.
• Thermometers use any property that varies regularly with temperature: the liquid-in-glass thermometer uses expansion of mercury or alcohol, the resistance thermometer uses electrical resistance of platinum, the thermocouple uses the emf between two different metals, and the constant-volume gas thermometer uses gas pressure.
• Mercury is chosen for thermometers because it is opaque and easily seen, expands uniformly, is a good conductor, does not wet glass, and has a wide range from -39 to 357 degrees Celsius. Alcohol is preferred in very cold regions because it freezes at about -112 degrees Celsius, well below the freezing point of mercury.
• Linear expansivity (alpha) is the fractional increase in length per degree rise in temperature. Area expansivity is 2 alpha and volume (cubic) expansivity is 3 alpha for the same solid.
• Expansion must be allowed for in engineering: gaps are left between rails and between bridge sections, telephone and transmission wires are hung slack, and a bimetallic strip of brass and iron bends on heating because brass expands more, which is how fire alarms and thermostats work.
• Water shows anomalous expansion between 0 and 4 degrees Celsius: it contracts as it is heated from 0 to 4 degrees and expands above 4. Water therefore has its maximum density at 4 degrees, which is why ice floats and why fish survive under a frozen pond surface.
• Heat capacity C is the heat needed to raise the temperature of a whole body by one kelvin, in J/K. Specific heat capacity c is the heat needed to raise unit mass by one kelvin, in J/kg/K, and Q = m c (theta2 - theta1). Water has an unusually high specific heat capacity of 4200 J/kg/K, which is why it is used as a coolant in car radiators.
• Latent heat is the heat absorbed or given out during a change of state at constant temperature. Specific latent heat of fusion is the heat needed to change unit mass of solid to liquid at its melting point; specific latent heat of vaporisation does the same from liquid to vapour. Use Q = m l, with no temperature term.
• In the method of mixtures, heat lost by the hot body equals heat gained by the cold body and the calorimeter, assuming no heat is lost to the surroundings. This single statement is the backbone of every calorimetry calculation.
• Boyle's law: at constant temperature, PV = constant, so P1V1 = P2V2. Charles's law: at constant pressure, V/T = constant, with T in kelvin. Pressure law: at constant volume, P/T = constant. Combining them gives the general gas equation P1V1/T1 = P2V2/T2.
• Evaporation occurs at all temperatures and only at the surface of the liquid, while boiling occurs throughout the liquid at one fixed temperature. Evaporation is increased by a larger surface area, higher temperature, moving dry air and lower pressure, and it causes cooling because the fastest molecules escape.
• Heat travels by conduction through solids as particles vibrate and pass energy on, by convection in fluids as warm, less dense regions rise and cooler regions sink, and by radiation as electromagnetic waves needing no material medium, which is how the sun reaches the earth.
• A vacuum flask blocks all three: the vacuum between the double walls stops conduction and convection, the silvered surfaces reflect radiation, and the cork or plastic stopper stops convection currents and conduction through the top. Dull black surfaces are the best absorbers and emitters of radiation; bright shiny surfaces are the worst.