Thermal Physics: 15 MCQs with answers

An object that absorbs all incident radiation and emits it perfectly

A black body is an idealized object that absorbs all incident electromagnetic radiation and emits radiation perfectly at all wavelengths.

A small hole in a cavity

A small hole in a cavity acts as a near-perfect black body because any radiation entering is absorbed after multiple reflections.

Max Planck

Max Planck introduced the quantum hypothesis in 1900 to explain the black body spectrum.

False

A black body emits a continuous spectrum of radiation across all wavelengths, with a peak that depends on temperature.

True

This is the Stefan-Boltzmann law: $E = \sigma T^4$.

Wien's displacement law

Wien's displacement law states that the peak wavelength is inversely proportional to temperature: $\lambda_{\text{max}} T = b$.

$T^4$

The Stefan-Boltzmann law states that the power radiated per unit area is $P = \sigma T^4$, where $\sigma$ is the Stefan-Boltzmann constant.

The spectral energy density of black body radiation

Planck's law gives the spectral radiance of a black body as a function of wavelength and temperature, resolving the ultraviolet catastrophe.

The failure of classical physics to explain the black body spectrum at short wavelengths

Classical Rayleigh-Jeans law predicted infinite energy at short wavelengths, which was resolved by Planck's quantum hypothesis.

$2.898 \times 10^{-3} \, \text{m·K}$

Wien's displacement constant $b$ is approximately $2.898 \times 10^{-3} \, \text{m·K}$.

16

Since $P \propto T^4$, doubling $T$ gives $2^4 = 16$ times the power.

Its temperature only

For a black body, emissive power depends solely on temperature, as described by Planck's law and Stefan-Boltzmann law.

A curve with a single peak

The spectrum is a continuous curve that rises to a peak at a certain wavelength and then falls off, with the peak shifting with temperature.

Kirchhoff's law

Kirchhoff's law of thermal radiation states that good absorbers are good emitters, and the ratio is the same for all bodies at a given temperature.

500 nm

Using Wien's law: $\lambda_{\text{max}} = b/T = (2.898 \times 10^{-3})/5800 \approx 5 \times 10^{-7} \, \text{m} = 500 \, \text{nm}$.