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A spherical block of dry ice at \(-79^{\circ} \mathrm{C}\) is exposed to atmospheric air at \(30^{\circ} \mathrm{C}\). The general direction in which the air moves in this situation is (a) horizontal (b) up \(\quad(c)\) down (d) recirculation around the sphere (e) no motion

Short Answer

Expert verified
Answer: (c) Down, as the cooler air molecules near the surface of the dry ice are denser and sink, pushing the warmer air molecules upward.

Step by step solution

01

Identify the temperature difference

There's a significant temperature difference between the dry ice (-79°C) and the atmospheric air (30°C). The air is warmer in comparison to the dry ice.
02

Understand the principle of convection

Convection is the transfer of heat within a fluid (in our case, air) due to the motion of the fluid. When air comes into contact with the dry ice, the air molecules near the surface of the dry ice lose energy and become cooler and denser. Because cool air is denser than warm air, it tends to sink.
03

Determine the direction of air flow

Due to the cooling effect of the dry ice, the air molecules nearest to it will become cooler and denser, causing them to sink. As these denser air molecules move downwards, they push the warmer air molecules, resulting in an upward flow of warm air. This sets up a continuous flow where cool air sinks and warm air rises.
04

Conclude the general direction of air movement

In conclusion, the general direction in which the air moves in this situation is: (c) down, as the cooler air molecules near the surface of the dry ice are denser and sink, pushing the warmer air molecules upward.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Convection
Convection is a fascinating heat transfer method that occurs in fluids such as gases and liquids. In the context of this exercise, it plays a vital role in how heat moves between the dry ice and the surrounding air. As the air around the dry ice gets cooled, the cooler, denser air molecules begin to sink, while the warmer, less dense molecules rise. This movement is due to the difference in density and creates a convection current.
These currents help distribute heat in the air and can be observed in everyday phenomena, such as boiling water, where you see bubbles and movement as the heat travels through the water.
  • Convection depends on fluid movement.
  • Density changes drive the movement in convection currents.
  • Common in both natural and artificial systems.
By understanding convection, we can better grasp how temperature changes affect gas and liquid behaviors, ultimately impacting everything from weather patterns to household heating systems.
Temperature difference
Temperature difference is the driving force behind various thermal phenomena, including convection. In this exercise, the substantial temperature difference between the dry ice (-79°C) and the surrounding air (30°C) leads to heat transfer.
When there's a big difference in temperature, heat transfers more rapidly. The greater the difference, the faster the heat tries to equalize between two areas. This difference motivates the movement of air molecules as they strive to balance the temperatures.
  • Larger temperature differences drive quicker heat transfer.
  • Creates conditions for convection to occur.
  • Affects the rate at which substances like dry ice sublimate.
The concept of temperature difference is central to many heating and cooling processes and helps explain why different materials and environments react differently to heat exposure.
Air flow direction
The direction of air flow is an essential aspect of how heat is transferred in the exercise scenario. With convection playing a central role, the air moves in a continuous cycle driven by temperature and density differences. When cold air from the dry ice surface becomes denser, it tends to sink towards the ground.
This sinking air displaces the warmer air, forcing it upward to maintain a cycle. The net effect is a circulation pattern with rising warm air and descending cool air. This flow direction contrasts with passive air movements, like diffusion, and is a more dynamic and predictable form of heat distribution.
  • Sinking cooler air facilitates convection currents.
  • Uplifting warmer air maintains the convection cycle.
  • Air flow direction impacts cooling and heating efficiency.
By understanding air flow direction, we can predict heat transfer outcomes more effectively, which is critical in many engineering and environmental applications.
Thermal properties
Thermal properties refer to how substances respond to temperature changes, which heavily influence convection and heat transfer. These properties include thermal conductivity, specific heat, and expansion/contraction rates.
In this exercise, the thermal properties of air allow it to circulate around the dry ice efficiently. Its relatively low thermal conductivity enables noticeable convection currents because heat does not spread instantaneously, allowing temperature gradients to exist.
  • Thermal conductivity: A measure of how well a material conducts heat.
  • Specific heat: The amount of heat needed to change a substance's temperature.
  • Thermal expansion: How a material's volume changes with temperature.
Understanding thermal properties provides insight into how different materials behave when exposed to temperature changes, aiding in designing systems that rely on heat transfer efficiencies, such as radiators, air conditioners, and refrigerators.

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Most popular questions from this chapter

A vertical \(1.5\)-m-high, 2.8-m-wide double-pane window consists of two layers of glass separated by a \(2.0\)-cm air gap at atmospheric pressure. The room temperature is \(26^{\circ} \mathrm{C}\) while the inner glass temperature is \(18^{\circ} \mathrm{C}\). Disregarding radiation heat transfer, determine the temperature of the outer glass layer and the rate of heat loss through the window by natural convection.

Under what conditions does natural convection enhance forced convection, and under what conditions does it hurt forced convection?

What does the effective conductivity of an enclosure represent? How is the ratio of the effective conductivity to thermal conductivity related to the Nusselt number?

Flat-plate solar collectors are often tilted up toward the sun in order to intercept a greater amount of direct solar radiation. The tilt angle from the horizontal also affects the rate of heat loss from the collector. Consider a \(1.5-\mathrm{m}\)-high and 3-m-wide solar collector that is tilted at an angle \(\theta\) from the horizontal. The back side of the absorber is heavily insulated. The absorber plate and the glass cover, which are spaced \(2.5 \mathrm{~cm}\) from each other, are maintained at temperatures of \(80^{\circ} \mathrm{C}\) and \(40^{\circ} \mathrm{C}\), respectively. Determine the rate of heat loss from the absorber plate by natural convection for \(\theta=0^{\circ}, 30^{\circ}\), and \(90^{\circ}\).

A solar collector consists of a horizontal aluminum tube of outer diameter \(5 \mathrm{~cm}\) enclosed in a concentric thin glass tube of \(7 \mathrm{~cm}\) diameter. Water is heated as it flows through the aluminum tube, and the annular space between the aluminum and glass tubes is filled with air at \(1 \mathrm{~atm}\) pressure. The pump circulating the water fails during a clear day, and the water temperature in the tube starts rising. The aluminum tube absorbs solar radiation at a rate of \(20 \mathrm{~W}\) per meter length, and the temperature of the ambient air outside is \(30^{\circ} \mathrm{C}\). Approximating the surfaces of the tube and the glass cover as being black (emissivity \(\varepsilon=1\) ) in radiation calculations and taking the effective sky temperature to be \(20^{\circ} \mathrm{C}\), determine the temperature of the aluminum tube when equilibrium is established (i.e., when the net heat loss from the tube by convection and radiation equals the amount of solar energy absorbed by the tube). For evaluation of air properties at \(1 \mathrm{~atm}\) pressure, assume \(33^{\circ} \mathrm{C}\) for the surface temperature of the glass cover and \(45^{\circ} \mathrm{C}\) for the aluminum tube temperature. Are these good assumptions?

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