Question

A hot object suspended by a string is to be cooled by natural convection in fluids whose volume changes differently with temperature at constant pressure. In which fluid will the rate of cooling be lowest? With increasing temperature, a fluid whose volume (a) increases a lot (b) increases slightly (c) does not change (d) decreases slightly (e) decreases a lot.

Short answer

Answer: (e) Fluid volume decreases a lot with temperature.

Step-by-step solution

Recall the principle of buoyancy

Buoyancy is the upward force exerted by a fluid that opposes the weight of a submerged object. The buoyancy force is caused due to the difference in pressure at different depths in a fluid, arising from the differences in fluid densities.

Analyze how fluid volume change affects buoyancy

As temperature increases, the fluid expands or contracts, resulting in different densities and therefore different buoyancy forces. More significant volume changes with temperature result in a more significant change in fluid densities and more effective natural convection heat transfer. Natural convection occurs when buoyancy-driven flow helps to remove heat from the hot object more effectively.

Compare each option to find the lowest rate of cooling

Now, let's compare each option: (a) Fluid volume increases a lot with temperature: This scenario has higher buoyancy-driven flow, leading to efficient heat transfer. (b) Fluid volume increases slightly with temperature: Here, buoyancy-driven flow is less significant, but some natural convection cooling may still occur. (c) Fluid volume does not change with temperature: This case means there's no buoyancy-driven flow, meaning cooling happens mainly through fluid conduction. (d) Fluid volume decreases slightly with temperature: In this case, fluid density increases, hindering buoyancy-driven flow which reduces the cooling effect. (e) Fluid volume decreases a lot with temperature: This case has the highest density increase, offering significant resistance to any buoyancy-driven flow, thereby further reducing the cooling effect.

Identify the lowest rate of cooling

Considering the analysis in step 3, option (e), where the fluid volume decreases a lot with temperature, will have the lowest rate of cooling because there is a significant resistance to buoyancy-driven flow, making the cooling effect minimal. So, the answer is (e).

Key concepts

Understanding Buoyancy Force

Imagine you're floating in a pool; you're experiencing buoyancy force. This is the same force that acts on objects submerged in a fluid, which could be as varied as the ocean or the air around us. In the context of natural convection cooling, buoyancy force is a key player.

Buoyancy arises because the pressure in a fluid changes with depth. The lower part of an object submerged in a fluid experiences greater pressure than the upper part, resulting in an upward force. It's not just any upward push, though. It's a carefully balanced act where the buoyancy force is exactly equal to the weight of the fluid that the object has displaced, as stated by Archimedes' principle.

When it comes to cooling a hot object suspended in fluid, buoyancy is what sets the fluid in motion away from the object. Warm fluid expands, becomes less dense, and rises, while cooler, denser fluid sinks to take its place. This movement helps to carry away the heat, chilling the hot object more efficiently. The greater the difference in density - which changes as the volume of the fluid expands or contracts with temperature changes - the stronger the buoyancy force, and the more effective the cooling process.

Fluid Density Changes and Their Impacts

When a fluid's temperature rises, it usually becomes less dense. Imagine a balloon expanding in the sun; that expansion is akin to fluid volume increasing with heat, causing density to drop. In the case of natural convection cooling, this behavior is critical.

Why does this matter? Because the degree of the fluid's density change affects the rate of cooling. If the fluid's volume noticeably increases with temperature (as in option (a) from the exercise), this creates a discernible drop in density. Conversely, if the volume decrease is substantial with a rise in temperature (option (e)), the fluid's density actually goes up. A fluid that doesn't see its volume change with temperature will not experience this density-driven buoyancy effect.

In essence, a fluid with no volume change with temperature won't assist in cooling through convection. It's the changing density that drives the fluid movement naturally, transferring heat away from the hot object. The greater the fluid volume changes, the more substantial the convection currents and the faster the cooling rate, all else being equal.

Heat Transfer Mechanisms in Context

Heat likes to spread out, and in natural convection cooling, there are three mechanisms at play: conduction, convection, and radiation. In the context of our hot object suspended by a string, let's focus on conduction and convection; radiation is usually concerning heat transfer without medium involvement, like the sun warming the Earth.

Conduction is the transfer of heat through a material without the movement of the substance itself, like a spoon heating up in a hot cup of tea. Convection, on the other hand, involves the physical movement of fluid, helping to redistribute heat, such as water boiling in a pot. In our suspended object scenario, if the fluid's volume doesn't change with temperature (option (c)), the heat transfer is primarily through conduction—the slowest mechanism of the three.

As for convection, when fluid density decreases with heat, it induces natural flows, aiding in the object's cooling. Fluids which experience greater changes in density with temperature will promote stronger convection currents and more efficient cooling. By understanding these mechanisms, students can grasp why a fluid that decreases a lot in volume with temperature would result in lower cooling rates and identify option (e) as the correct answer to the exercise.