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Thermal energy transfer IB DP Physics Study Notes

Thermal energy transfer IB DP Physics Study Notes - 2025 Syllabus

Thermal energy transfer IB DP Physics Study Notes

Thermal energy transfer IB DP Physics Study Notes at  IITian Academy  focus on  specific topic and type of questions asked in actual exam. Study Notes focus on IB Physics syllabus with Students should understand

  • that conduction, convection and thermal radiation are the primary mechanisms for thermal energy transfer
  • conduction in terms of the difference in the kinetic energy of particles
  • quantitative analysis of rate of thermal energy transfer by conduction in terms of the type of material and cross-sectional area of the material and the temperature gradient as given by $\frac{\Delta Q}{\Delta t}=k A \frac{\Delta T}{\Delta x}$ qualitative description of thermal energy transferred by convection due to fluid density differences quantitative analysis of energy transferred by radiation as a result of the emission of electromagnetic waves from the surface of a body, which in the case of a black body can be modelled by the Stefan Boltzmann law as given by $L=\sigma A T^4$ where $L$ is the luminosity, $A$ is the surface area and $T$ is the absolute temperature of the body
  • the concept of apparent brightness $b$
  • luminosity $L$ of a body as given by $b=\frac{L}{4 \pi d^2}$
  • the emission spectrum of a black body and the determination of the temperature of the body using Wien’s displacement law as given by $\lambda_{\max } T=2.9 \times 10^{-3} \mathrm{mK}$ where $\lambda_{\max }$ is the peak wavelength emitted.

Standard level and higher level: 6 hours
Additional higher level: There is no additional higher level content

IB DP Physics 2025 -Study Notes -All Topics

Conduction

  • Thermal energy can be transferred from a warmer mass to a cooler mass by three means: conduction, convection, and radiation.
  • This energy transfer is called heating and cooling.
  • Only thermal radiation transfers heat without any physical medium such as solid, liquid or gas.

EXAMPLE:

The heat from a wood-burning stove can be felt from all the way across the room because photons carrying infrared energy can travel through empty space. When these photons strike you, they are absorbed as heat. This process of thermal energy transfer is called thermal radiation.

  • When two objects of different temperatures touch, thermal energy is transferred from the hotter object to the cooler object through a process called conduction.
  • When atoms of one portion of a medium are in contact with vibrating atoms of another portion, the vibration is transferred from atom to atom.

High T portions vibrate more than low T portions, so we can imagine the vibration “impulse” to travel through the material, from high T to low T.

  •  Metals are good heat conductors because they have lots of free electrons (the same reason they are good electrical conductors).
  • The rate $\frac{\Delta Q}{\Delta t}$ at which heat energy is transferred depends directly on the cross-sectional area $A$ and inversely with the length $d$ of the conductor.

That rate, $\frac{\Delta Q}{\Delta t}$, is also proportional to the difference in temperature $\Delta T$, between the two ends.

$\frac{\Delta Q}{\Delta t}=k A \frac{\Delta T}{\Delta x}\quad \text{thermal conduction}$

  • Consider a material that acts as a conductor of heat from the hot object to the cold object.

  • During the process the hot object loses energy and cools, while the cold object gains energy and warms.
  • At the end of the process the two ends have reached thermal equilibrium at which point there is no more net transfer of heat.

Convection

  • Another form of heat transfer is called convection.
  • Convection requires a fluid (liquid or gas) as a medium of heat transfer.
  • For example, hot air is less dense than cold air, so it rises.
  • But as it rises it cools, and so becomes denser and sinks.
  • We thus obtain a cycle, which forms a circulation called a convection current.
  • ∙

Black-body radiation

  • Solids can absorb many more wavelengths than the atmospheric gases.
  • Depending on the color of a solid you can determine what wavelengths it cannot absorb.
  • For example, a green object reflects (and therefore does not absorb) green light.
  • A black object absorbs all wavelengths.
  • A black-body absorbs all wavelengths. As it heats up it emits all wavelengths, called black-body radiation
  • Solids can be heated to incandescence (glowing) and different temperatures will have different visible radiation.
  • If we heat a black-body to incandescence we observe:

Two trends emerge:

  • The higher the temperature the greater the intensity at all wavelengths.
  •  
  • The higher temperature the smaller the wavelength of the maximum intensity.
  • A simple law called Wein’s displacement law tells us the wavelength of the maximum intensity λmax for blackbodies at temperature T in Kelvin:

$\lambda_{\max } T=2.90 \times 10^{-3} \mathrm{mK} \quad$ Wien’s displacement law

The Stefan-Boltzmann law

Without proof, the Stefan-Boltzmann law is as follows:

$$ E \propto T^4 \Rightarrow E=\sigma T^4 \text { for perfectly black body } $$

where $E$ is energy emitted per second from unit surface area of the black body, T is temperature and $\sigma$ is Stefan’s constant, and

$$ \sigma=5.67 \times 10^{-8} \mathrm{Wm}^{-2} \mathrm{~K}^{-4} $$

$\sigma$ is called the Stefan-Boltzmann constant.

The Stefan-Boltzmann law shows the relationship between the temperature of a black-body and the power emitted by the black-body’s surface area.

FYI

  • A black-body emits as much power as it absorbs.
  • Thus the Stefan-Boltzmann law works for both emission and absorption problems.
  • Since no body is at absolute zero (K = 0) it follows from the Stefan-Boltzmann law that all bodies radiate.
  • Be sure that T is in Kelvin, not Celsius.

 

Luminosity

  • The energy radiated by a star is emitted uniformly in all directions, just as we would see with a light bulb
  • The total energy emitted by the star per unit time (i.e. the power) is called the luminosity of the star, L. Our Sun has a luminosity of 3.90 x 1026W
  • We can measure brightness and determine distance to learn the luminosity of a star. (as you will see)
  • Luminosity is based on radius and temperature of a star.
  • If r is equal, then higher temp = higher L
  • If temp is equal, then greater r = higher L

Determining Distances

 

  • Allow for a comparison of the Luminosities of different stars
  • A is the surface area of the star (SA of a sphere is $4 \pi r^2$ )
  • $T$ is the surface temperature of the star
  •  $\sigma$ is the Stefan-Boltzmann Constant $=5.67 \times 10^{-}$ ${ }^8 \mathrm{Wm}^{-2} \mathrm{~K}^{-4}$
  • R is the radius of the Star From this we can see that the luminosity of a star depends on it’s temperature and size!

Apparent Brightness

  • By the time the energy released by a star arrives at Earth it will be spread out over a sphere of radius d. 
  • The energy received per unit time per unit area at the Earth is called the apparent brightness, b

  • Assuming two stars of equal L, the closer star has a greater brightness

  • We would have to know the L of a star and its brightness to determine distance, but since all stars are not equally bright or luminous, we cannot use the formula in that way.

  • However, using the Stephan-Boltzman Law, we can determine luminosity and then use the luminosity value and apparent brightness to determine distances.

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