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: (c) A fluid whose volume does not change with increasing temperature.

Step-by-step solution

Understanding convection

In natural convection, the rate of cooling depends on the flow of heat from the hot object to the surrounding fluid, as well as the fluid's ability to move and carry the heat away from the object. The motion of the fluid is caused by density changes due to temperature differences. Fluids with a lower density tend to rise, while those with a higher density tend to sink. This movement creates a circulation, allowing heat transfer to occur in the fluid, and thus cooling the hot object.

Effect of volume changes on convection

When a fluid's volume changes with temperature, it affects the fluid's density, and thus the flow of heat through convection. Let's examine the given options one by one: (a) A fluid whose volume increases a lot with increasing temperature: In this case, the fluid will have a lower density when its temperature increases, causing it to rise. This will enhance the overall convection process and the circulation of fluid, which in turn will result in a faster rate of cooling. (b) A fluid whose volume increases slightly with increasing temperature: Similar to option (a), the fluid will have a lower density as temperature increases, but the change will be less significant. This will still result in some circulation and convection, but at a slower rate than option (a). (c) A fluid whose volume does not change with temperature: Here, the fluid's density will remain constant at different temperatures. Consequently, there will be no circulation due to density differences, and thus no cooling through convection. (d) A fluid whose volume decreases slightly with increasing temperature: In this case, the fluid will have a higher density when its temperature increases, causing it to sink. This will result in some circulation, but in the opposite direction of the typical convection process, disrupting the heat transfer and slowing down the cooling rate. (e) A fluid whose volume decreases a lot with increasing temperature: Similar to option (d), the fluid will have a higher density as temperature increases, causing it to sink at an even faster rate. This will significantly disrupt the convection process, making it less efficient in cooling the hot object.

Determining the lowest rate of cooling

Based on our analysis, the fluid with the lowest rate of cooling will be the one with no cooling through convection, as it has no circulation due to density differences. Therefore, the correct answer is (c) a fluid whose volume does not change with increasing temperature.