Thermal Properties of Matter: common doubts, answered
The questions students ask most often about Thermal Properties of Matter, each with a short answer. For the full chapter, read the Thermal Properties of Matter notes.
Temperature, heat and thermometer scales
Read this section in the notes →What is the difference between heat and temperature?
Temperature measures how hot or cold a body is and decides which way energy flows between two bodies in contact. Heat is the energy that actually transfers because of a temperature difference. A bathtub of warm water holds far more internal energy than a red-hot pin, yet the pin has the higher temperature.
How do you convert a temperature change from Celsius to Fahrenheit?
Multiply by 9/5 and do not add 32. The offset of 32 matters only for converting an actual temperature reading, since the two scales start at different points. A change of 10 °C is a change of 18 °F, and a change of 10 °C is exactly a change of 10 K, because the kelvin and Celsius degree are the same size.
Ideal-gas equation and absolute temperature
Read this section in the notes →Why is absolute zero −273.15 °C?
For a fixed amount of a low-density gas held at constant volume, the pressure falls in a straight line as the gas is cooled. Extending this line back to zero pressure gives the same temperature for every gas, about −273.15 °C. This is taken as absolute zero, the starting point of the kelvin scale, so T = t_C + 273.15.
Thermal expansion
Read this section in the notes →What is the relation between coefficients of linear and volume expansion?
For an isotropic solid, the coefficient of volume expansion is about three times the linear coefficient: α_V = 3α_l. This is because the solid expands equally in all three directions. Each length grows by the fraction α_l ΔT, so the volume grows by roughly three times that fraction for small temperature changes.
Why are gaps left between railway tracks?
Steel rails expand on hot days, by Δl = l α_l ΔT. Without gaps, the expanding rails would push against each other and buckle. The small gaps give the rails room to lengthen safely. The same reasoning explains expansion joints in bridges and concrete roads.
Anomalous expansion of water and thermal stress
Read this section in the notes →At what temperature is water densest?
Water is densest at about 4 °C, not at 0 °C. Between 0 °C and 4 °C water contracts on heating, which is unusual, and above 4 °C it expands like other liquids. This anomalous behaviour is why the bottom of a frozen lake stays at around 4 °C.
Why do lakes freeze from the top down?
As the surface water cools below 4 °C it becomes less dense, so it stays on top instead of sinking. It freezes at the surface first, and ice is less dense than water, so it floats. The ice layer then insulates the water below, which stays near 4 °C and lets aquatic life survive the winter.
What is thermal stress?
Thermal stress is the stress that builds up in a rod or beam that is heated or cooled while its ends are held fixed so it cannot change length. It equals Y α ΔT, and the force on the supports is Y A α ΔT. This can be large enough to buckle rails or crack materials.
Specific heat capacity
Read this section in the notes →What is the difference between heat capacity and specific heat capacity?
Heat capacity S = ΔQ/ΔT is the heat needed to raise a particular body by one kelvin, so it depends on how much material there is. Specific heat capacity s is the heat needed per unit mass, making it a property of the material alone. Molar specific heat C is the same idea per mole.
Why does water heat up and cool down slowly?
Because water has an unusually high specific heat capacity, about 4186 J kg⁻¹ K⁻¹. A large amount of heat changes its temperature only a little. This makes water a good coolant in car radiators and a good store of heat in hot-water bags, and it is why coastal areas have milder climates.
Calorimetry
Read this section in the notes →What is the principle of calorimetry?
In an isolated system with no heat lost to the surroundings, heat lost by the hotter bodies equals heat gained by the colder ones. When a hot metal is dropped into water in a calorimeter, the heat given out by the metal raises the temperature of the water and the calorimeter until all reach a common final temperature.
Change of state
Read this section in the notes →Why does temperature stay constant while ice melts?
Because all the heat supplied during melting goes into breaking the bonds that hold the solid together, not into raising the speed of the molecules. Until all the ice has melted, the temperature of the ice-water mixture stays at the melting point. So Q = msΔT cannot be used during a change of state; use Q = mL instead.
Why does pressure change the boiling point of water?
A liquid boils when its vapour pressure equals the surrounding pressure. Raising the pressure means a higher temperature is needed before this happens, so the boiling point rises. That is why a pressure cooker cooks faster. At high altitudes the lower air pressure lowers the boiling point, so food takes longer to cook.
Latent heat
Read this section in the notes →Why does steam at 100 °C cause worse burns than water at 100 °C?
Because steam releases its latent heat of vaporisation, about 2.26 × 10⁶ J kg⁻¹, when it condenses on the skin, before it even begins to cool. Boiling water at the same temperature has no such extra energy to release. So the same mass of steam delivers far more heat to the skin.
How do you know whether all the ice melts in a mixing problem?
First calculate the heat needed to melt all the ice, mL, and compare it with the heat the warm water can give in cooling to 0 °C. If the water can supply enough, all the ice melts and the final temperature is above 0 °C. If not, only part of the ice melts and the final temperature is 0 °C.
Conduction
Read this section in the notes →How do you find the equivalent conductivity of two rods in series?
For two rods of equal length and area joined end to end, the same heat current passes through both, so their thermal resistances L/(KA) add. The equivalent conductivity is then K′ = 2K₁K₂/(K₁ + K₂), not the sum K₁ + K₂ and not the simple average. If the same two rods are placed side by side instead, their heat currents add and the equivalent conductivity is (K₁ + K₂)/2.
Why do cooking pans have copper bottoms?
Copper is a very good conductor of heat, so a copper base spreads heat evenly across the bottom and passes it to the food quickly. The rate of heat flow through a layer, H = K A (T_C − T_D)/L, grows with the conductivity K, so a high-K material makes heating faster and more uniform.
Convection
Read this section in the notes →Why can't convection take place in solids?
Convection needs the material itself to move, carrying heat with it as warmer, less dense parts rise and cooler parts sink. In a solid the particles are held in place and cannot flow, so heat can only travel by conduction or, if transparent, radiation. Convection happens only in liquids and gases.
Radiation and blackbody radiation
Read this section in the notes →What is Wien's displacement law used for?
It relates the wavelength at which a black body emits most strongly to its temperature: λ_m T = 2.9 × 10⁻³ m K. Hotter bodies peak at shorter wavelengths. Measuring the peak wavelength of sunlight gives the temperature of the Sun's surface, around 6000 K, not its much hotter interior.
Why must temperature be in kelvin in Stefan's law?
Because Stefan's law, H = A e σ T⁴, makes the emitted power proportional to the fourth power of absolute temperature. A body at 0 °C still radiates, since it is at 273 K, so using Celsius would give zero or nonsense. Always convert to kelvin before raising to the fourth power.
Newton's law of cooling
Read this section in the notes →When does Newton's law of cooling apply?
It applies when the temperature difference between a body and its surroundings is small. Then the rate of cooling is proportional to that difference: −dQ/dt = k(T₂ − T₁). For a large difference, radiation losses grow much faster than linearly and the law becomes inaccurate. Over an interval, use the average temperature of the body.
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