CDS Physics · Formula sheet
Heat and Thermodynamics formulas
3 formulas, 2 reference tables and 10 common traps for CDS Physics Heat and Thermodynamics, grouped by subtopic.
Temperature and Heat Transfer
Learn this subtopic in the notesTemperature scales: Kelvin, Celsius and Fahrenheit
Converting between temperature scales
- temperature in kelvin
- temperature in degrees Celsius
- temperature in degrees Fahrenheit
Specific heat and the principle of calorimetry
Heat for a temperature change, and the calorimetry balance
- heat taken in or given out, in joules
- mass, in kg
- specific heat of the material
- change in temperature
- the common final temperature of the mixture
Conduction, convection and radiation
| Everyday case | Main mode of heat transfer |
|---|---|
| Heating one end of a brass rod warms the other end | Conduction |
| Water boiling in a pot on a gas stove | ConvectionQ CDS 2024 (II): boiling water in a pot is the example of convection. |
| Land and sea breezes | Convection |
| Warm air circulating round a blast furnace | Convection |
| Feeling the warmth of the Sun | Radiation |
| Glass of an electric bulb heated by the glowing filament | RadiationQ CDS 2018 (II): this is the one case in a list that is not convection. |
| Thermal conductivity, highest to lowest | Copper, aluminium, water, hydrogen gasQ CDS 2026 (I): hydrogen gas has the least thermal conductivity of these four. |
| Cooling a hot bowl of rice fast | Stand it in water and run a fan at full speedQ CDS 2024 (I): a water bath with a fast fan beats still air, a cooled room or water alone. |
Common traps
Add 273 to go from Celsius to Kelvin, never subtract
The Kelvin number is always the bigger one, because the Kelvin scale starts lower, at absolute zero. So . A relation such as or gives a negative Kelvin reading for a warm day, which is impossible.
The Fahrenheit constant is 32, and the factor is 9/5
Ice melts at 32 °F, so the constant added is 32, not 36. Each Celsius degree is 9/5 of a Fahrenheit degree, so the factor is 9/5, not 5/9 or 10/3. Check any formula with one point: 100 °C must give 212 °F.
A microwave oven does not heat by convection
The microwaves are absorbed by the water in the food, which heats the food from within. That is heating by radiation absorbed in the food, not by moving hot air. Convection needs a fluid that flows and carries the heat.
Every gas is a poor conductor, even the best one
Hydrogen conducts heat better than any other gas, but every gas conducts far less than water, and water far less than a metal. A question asking for the least conductor among metals, water and a gas wants the gas.
Radiation needs no medium; conduction and convection do
The Sun's heat crosses empty space, so it must be radiation. Conduction needs a material to pass through, and convection needs a fluid that can flow.
Calorimetry and thermal equilibrium are not the same name
Heat lost = heat gained is the principle of calorimetry. Thermal equilibrium is only the final state, when the two temperatures have become equal. A question asking for the relation 'heat lost = heat gained' wants calorimetry.
Change of State and Gases
Learn this subtopic in the notesLatent heat, evaporation and the triple point
Heat for a change of state
- heat taken in or given out, in joules
- mass that changes state, in kg
- latent heat of fusion or of vaporisation, in J/kg
The ideal gas and thermodynamic processes
| Process | What stays constant |
|---|---|
| Isothermal | Temperature |
| Isobaric | Pressure |
| Isochoric | Volume |
| Adiabatic | No heat flows in or out of the gas |
| Joule-Thomson throttling | Enthalpy (an isoenthalpic process) |
Common traps
Latent heat changes the state, not the temperature
During melting or boiling the temperature stays fixed until the whole mass has changed state. Use for that stage and only for the stages where the temperature changes.
The triple point is 273.16 K, not 273.15 K or 0 K
Ice, water and vapour coexist at 273.16 K and about 611 Pa. The ice point at normal pressure is 273.15 K, a hundredth of a degree lower. Any option with 0 K or 373 K for the triple point is wrong.
Equal average energy does not mean equal speeds
At one temperature the molecules of a gas have one average kinetic energy, but individual molecules move at many different speeds. A statement that all the molecules move at the same speed is false even for an ideal gas.
Isochoric is volume, isobaric is pressure
Iso means 'equal'. Isobaric keeps the pressure (bar) fixed, isochoric keeps the volume fixed, isothermal keeps the temperature fixed. Match the root before choosing.