ONE-EIGHTH STAGE 2024
ONE-EIGHTH STAGE, ROUND 5 RIDDLES
Ampraeso SHS: 35 points (winner, qualified to the quarterfinal stage)
Anlo SHS: 31 points
Mfantsiman Girls SHS: 27 points
ROUND 5 - RIDDLE
RIDDLE
I am a named law in physics.
I am a thermophysical law.
I contain a physical constant whose value depends on the reciprocal of the speed of light squared.
I am a power-versus-temperature law.
I am the law that expresses the relationship between radiated power and the fourth power of absolute temperature.
Who am I?
ANSWER: Stefan's law (Stefan-Boltzmann law)
EXPLANATION:
The Stefan-Boltzmann law, $P=\sigma AT^4$, relates radiated power to the fourth power of absolute temperature, where $\sigma$ is the Stefan-Boltzmann constant, whose defining expression contains $\dfrac{1}{c^2}$.
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PRACTICE QUESTIONS
1. RIDDLE:
I am a law of thermal radiation.
I tell you where a hot body's spectrum peaks.
The peak wavelength and the absolute temperature have a constant product.
My constant is about $2.9\times10^{-3}$ m K.
Hotter bodies glow bluer because of me.
I am named after a German physicist who won the 1911 Nobel Prize.
Who am I?
ANSWER: WIEN'S LAW
EXPLANATION:
$\lambda_{max}T = b$, with $b \approx 2.9\times10^{-3}$ m K.
2. RIDDLE:
I am a law of thermal radiation.
I give the whole spectrum of a black body.
I assume energy comes in quanta $hf$.
I removed the ultraviolet catastrophe.
I was proposed in 1900.
Quantum theory began with me.
Who am I?
ANSWER: PLANCK'S LAW
EXPLANATION:
Planck's radiation law fits the black-body spectrum at all wavelengths by quantising energy.
3. RIDDLE:
I am a law about heat loss.
I say a body loses heat at a rate proportional to how much hotter it is than its surroundings.
I work well when that difference is small.
My temperature-time curve is exponential.
A cup of tea obeys me.
I am named after the scientist of gravitation.
Who am I?
ANSWER: NEWTON'S LAW OF COOLING
EXPLANATION:
$\dfrac{dT}{dt} = -k(T - T_s)$ for small temperature differences.
4. RIDDLE:
I am a law about how bodies take in and give out heat.
I say good absorbers are good emitters.
At equilibrium a body's emissivity equals its absorptivity.
I explain why a black kettle cools faster.
I share my author with rules for electric circuits.
I was stated in 1859.
Who am I?
ANSWER: KIRCHHOFF'S LAW OF THERMAL RADIATION
EXPLANATION:
Emissivity equals absorptivity at each wavelength for a body in thermal equilibrium.
5. RIDDLE:
I am a classical radiation law.
I work well at long wavelengths.
I predict infinite energy at short wavelengths.
I treat energy as continuous.
I am named after two British physicists.
Planck's law replaced me.
Who am I?
ANSWER: RAYLEIGH-JEANS LAW
EXPLANATION:
Classical physics gives $I \propto \dfrac{T}{\lambda^4}$, which fails at short wavelengths.
6. RIDDLE:
I am a failure of classical physics.
I was predicted for short wavelengths.
I would make a black body radiate infinite energy.
Quantisation of energy removed me.
My name points to the violet end and beyond.
My name also suggests a disaster.
Who am I?
ANSWER: ULTRAVIOLET CATASTROPHE
EXPLANATION:
The Rayleigh-Jeans law predicts unlimited emission at short wavelengths; Planck's quanta solve it.
7. RIDDLE:
I am a number between 0 and 1.
I compare a surface's radiation with that of a black body.
A perfect black body has 1 for me.
Polished silver has a very small value of me.
I appear in $P = e\sigma AT^4$.
Good absorbers have a large value of me.
Who am I?
ANSWER: EMISSIVITY
EXPLANATION:
Emissivity is the ratio of a surface's radiated power to that of a black body at the same temperature.
8. RIDDLE:
I am an instrument.
I measure very high temperatures.
I do not touch the hot object.
I compare the colour or brightness of its glow.
Furnaces and molten metals are measured with me.
My name comes from the Greek for fire.
Who am I?
ANSWER: PYROMETER
EXPLANATION:
An optical pyrometer finds temperature from the radiation a hot body emits.
9. RIDDLE:
I am an early idea about heat exchange.
I say every body radiates, whatever its temperature.
A body at the same temperature as its surroundings gives and takes equally.
I explain why a body in equilibrium stays at constant temperature.
I was proposed in 1791.
I am named after a Swiss physicist.
Who am I?
ANSWER: PREVOST'S THEORY OF EXCHANGES
EXPLANATION:
Bodies continually emit and absorb radiation; equilibrium means equal rates.