Assertion: If liquid in a container is heated at top rather...

Assertion: If liquid in a container is heated at top rather than at the bottom. The main process by which the rest of the liquid becomes hot is conduction. Reason: Two spheres of the same material have radii $a$ and $2 a$, temperature $2 T$ and $T$, respectively. The energy radiated per second by the first sphere is greater than that of the second. (A) $\mathrm{A}$ (B) $\mathrm{B}$ (C) $\mathrm{C}$ (D) D

Assertion: If liquid in a container is heated at top rather than at the bottom. The main process by which the rest of the liquid becomes hot is conduction. Reason: Two spheres of the same material have radii $a$ and $2 a$, temperature $2 T$ and $T$, respectively. The energy radiated per second by the first sphere is greater than that of the second.
(A) $\mathrm{A}$
(B) $\mathrm{B}$
(C) $\mathrm{C}$
(D) D

Key Concepts

Thermal Conduction

Thermal conduction is the process by which heat is transferred through a material via direct contact, with energy moving from higher to lower temperature regions through molecular collisions or electron movement. This mechanism is typically slower in fluids unless the temperature gradients are very steep or the material properties favor rapid energy transfer.

Convection in Fluids

Convection is a mode of heat transfer where heat is carried by the motion of the fluid. When a fluid is heated from below, less dense hot fluid rises and cooler fluid sinks, creating convective currents that efficiently transport heat. The question hints at the difference in behavior when heating from the top, where such convective currents can be suppressed or even inverted, making conduction more significant instead.

Radiative Heat Transfer

Radiative heat transfer involves the emission or absorption of electromagnetic radiation, mainly in the infrared range, by a body due to its temperature. Unlike conduction and convection, radiation does not require a medium to transfer energy, and its efficiency heavily depends on the temperature and emissivity of the radiating surface.

Stefan-Boltzmann Law

The Stefan-Boltzmann law quantifies the power radiated per unit area of a black body in terms of its temperature, stating that the energy radiated per unit area is proportional to the fourth power of the temperature. This principle is key when comparing radiative heat loss from objects of different temperatures and sizes, as even small differences in temperature can lead to large differences in radiative power.

Scaling Laws in Thermal Radiation

Scaling laws in thermal radiation refer to how physical quantities such as surface area and temperature influence the energy emitted by an object. For instance, a sphere’s radiative output scales with its surface area (which is proportional to the square of its radius) and with the fourth power of its temperature, highlighting non-linear dependencies that are often used to compare the radiative efficiencies of bodies with different sizes and temperatures.

Transcript

00:01 In the given question, we're given a reason statement and an assertion statement and we have to find out whether the statements are true or not.

00:09 So firstly, we'll look at the assertion statement.

00:12 So according to this statement, it says that if liquid in a container is heated at top rather than the bottom.

00:18 So if we have a liquid container over here and it is heated from the top rather than the bottom.

00:25 So in this case, the main process by which the rest of the liquid becomes hot is conduction.

00:30 So we have to find out whether it's conduction or its convection.

00:34 So firstly, we need to know that whenever a liquid gets is heated.

00:38 So if it's getting heated from the top, all the particles over here float by, they all will become less denser.

00:46 So they'll become lighter, in fact.

00:48 So the gravity will not pull it down, but they will remain up only.

00:54 So because of this, they will not move downwards and the heavier ones will remain down.

00:59 So there's no situation of the formation of convection current here.

01:04 So the main process here will be conduction.

01:08 So our first statement, which is the assertion statement, stands true.

01:14 So we can declare the statement as true.

01:16 Now moving on to the second statement, which is a reason statement...

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