Q.'Gulab Jamuns' (assumed to be spherical) are to be heated in an oven. They are available in two sizes, one twice bigger (in radius) than the other. Pizzas (assumed to be discs) are also to be heated in oven. They are also in two sizes, one twice big (in radius) than the other. All four are put together to be heated to oven temperature. Choose the correct option from the following: (Note: more than one of the given options may be correct.)

Thermal Radiation Properties

Imagine holding your hand near a hot iron — you feel warmth without touching it. That warmth travels through empty space, not through air or metal. This is thermal radiation: energy emitted by any object purely because it has a temperature.

Unlike conduction (touching) or convection (fluid flow), radiation doesn't need a medium. It's electromagnetic waves — mostly infrared, but at high temperatures, visible light too. A glowing red-hot steel rod is radiating; so is your own body, though you can't see it.

The Core Idea: Every Object Radiates

Every object above absolute zero ($0\ \text{K}$) emits radiation. The amount and type depend on two things:

1. Temperature — hotter objects radiate more energy, and at shorter wavelengths.
2. Surface properties — some surfaces are good emitters, others are poor.

This leads to three key properties that describe how a real surface behaves compared to an ideal "perfect" radiator.

1. Emissivity ($\varepsilon$)

Intuition: A black matte surface feels hotter in sunlight than a shiny white one. Why? The black surface emits radiation more efficiently.

Definition: Emissivity is the ratio of radiation emitted by a real surface to the radiation emitted by an ideal blackbody at the same temperature.

• $\varepsilon = 1$ for a perfect blackbody (ideal emitter).
• $0 < \varepsilon < 1$ for all real surfaces.
• $\varepsilon$ depends on material, surface finish, and wavelength.

2. Absorptivity ($\alpha$)

Intuition: A black car roof gets hotter in summer than a white one. It absorbs more sunlight.

Definition: Absorptivity is the fraction of incident radiation that a surface absorbs.

• $\alpha = 1$ for a perfect blackbody (absorbs everything).
• $\alpha = 0$ for a perfect reflector.
• For opaque surfaces: $\alpha + \rho = 1$, where $\rho$ is reflectivity.

3. Reflectivity ($\rho$) and Transmissivity ($\tau$)

Intuition: A mirror reflects; a glass window transmits; a brick wall does neither.

Definition: For any surface, incident radiation is either absorbed, reflected, or transmitted:

• Reflectivity $\rho$: fraction reflected.
• Transmissivity $\tau$: fraction transmitted through.
• For opaque solids: $\tau = 0$, so $\alpha + \rho = 1$.

The Blackbody: The Ideal Reference

A blackbody is a theoretical surface that:

• Absorbs all incident radiation ($\alpha = 1$).
• Emits the maximum possible radiation at any temperature.
• Follows Planck's law, Stefan-Boltzmann law, and Wien's displacement law.

Real surfaces are compared to this ideal. The blackbody is a standard — like comparing a real engine to a Carnot engine.

Putting It Together: A Real Surface

A hot metal plate at $500\ \text{K}$ with $\varepsilon = 0.3$ emits:

$E = 0.3 \times 5.67 \times 10^{-8} \times (500)^4 \approx 1063\ \text{W/m}^2$ …