What distinguishes a grey body from a real body?

A grey body has emissivity less than 1 that does not depend on wavelength; a real body's emissivity varies with wavelength, temperature and direction

A grey body absorbs all radiation; a real body absorbs none

A grey body has zero emissivity; a real body has emissivity 1

A grey body transmits all radiation; a real body reflects all

In the proof of Kirchhoff's law, the small body is placed in a black enclosure at the same temperature. Why does EA = alpha E_b A?

Because at thermal equilibrium there is no net heat flow, so emitted energy equals absorbed energy

Because the body is a black body

Because the enclosure is hotter than the body

Because the body reflects all radiation

Emissivity of a surface is defined as

the ratio of its emissive power to that of a black body at the same temperature

the fraction of incident radiation absorbed

the ratio of reflected to incident radiation

the emissive power at the peak wavelength

Practice · 5 marks

Radiation properties and black and grey bodies

Short answer

Absorptivity α, reflectivity ρ, transmissivity τ satisfy α+ρ+τ=1. Black body: α=ε=1; grey: ε<1 constant; real: ε varies with λ. Emissivity ε = E/E_b. Kirchhoff's law: at thermal equilibrium, ε=α, proved by placing a small body in a black enclosure at same T, energy balance gives EA = α E_b A, so ε=α.

Define absorptivity, reflectivity and transmissivity and show how they are related. Differentiate between a black body, a grey body and a real body. What is emissivity? State and prove Kirchhoff's law for total radiation.

Radiation properties

When radiation of total amount $G$ (irradiation) strikes a surface, part is absorbed, part reflected and part transmitted:

Absorptivity $\alpha$ = fraction absorbed.
Reflectivity $\rho$ = fraction reflected.
Transmissivity $\tau$ = fraction transmitted.

\alpha + \rho + \tau = 1

For an opaque solid $\tau = 0$ , so $\alpha + \rho = 1$ . For a black body $\alpha = 1$ ; for a white body $\rho = 1$ ; for a transparent body $\tau = 1$ .

Types of bodies

Body	Property
Black	Absorbs all radiation, $\alpha = 1$ , $\varepsilon = 1$ ; emits maximum at each $\lambda$ and $T$
Grey	Emissivity $\varepsilon<1$ independent of wavelength; emits a constant fraction of black body
Real	$\varepsilon$ and $\alpha$ vary with wavelength, temperature and direction

Emissivity $\varepsilon = E/E_b$ is the ratio of the emissive power of a surface to that of a black body at the same temperature.

Kirchhoff's law (proof)

Place a small body of area $A$ , emissive power $E$ and absorptivity $\alpha$ inside a black enclosure at the same temperature $T$ . The enclosure sends radiation $E_b$ per unit area on the body, of which the body absorbs $\alpha E_b A$ . It emits $EA$ . At thermal equilibrium (no net heat flow, since temperatures are equal):

EA = \alpha E_b A\;\Rightarrow\;\frac{E}{E_b} = \alpha \;\Rightarrow\; \varepsilon = \alpha

Thus at the same temperature the emissivity of a body equals its absorptivity.

✓ Answer checked by Claude Sonnet 5.5

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