# Heat Transferred to a Falling Object

• Comeback City
The temperature is proportional to the pressure and inversely proportional to the altitude. So, the higher up you go, the lower the temperature.

#### Comeback City

If I was attempting to calculate the amount of energy transferred as heat to an object free-falling in the atmosphere, is this how I could go about it?...

Work = (Drag Force) x (Displacement through atmosphere) = Energy transferred as Heat

I am attempting to solve a hypothetical question which goes, if a small ice cube is dropped from 30,000 feet in the air, will it melt before it hits the ground? After finding the energy transferred to the ice cube, I would calculate the amount of energy (using specific heat of H2O) required to both raise the temperature of the ice to 0 degrees and then to change the phase of the ice to liquid water, and compare it to the amount of energy transferred from the fall. Does this process seem to check out?

No, because the air can heat up rather than the ice cube getting heated.

berkeman
No, because the air can heat up rather than the ice cube getting heated.
Thanks for the response!
Is there a way to tell whether or not the air would heat up rather than the ice cube heating up? If not, is there a way to solve this problem?

There is one additional complicating factor, in that, if there is evaporation that takes place from the liquid converting to gas, the result is 540 calories/gram. In general, the ice cube problem, in my estimation, does not have a simple solution. ## \\ ## Clearly, without even calculating it, the change in gravitational potential is enough to completely vaporize the ice cube, but whether it results in air getting heated and/or in kinetic energy of the ice cube is another matter. ## \\ ## Scratch this last statement: Let's compute it: ## U=mgh ## , ## h=30,000 ## ft ## \approx 9,000 ## meters, ## g=9.8 ## m/sec^2 , and ##m=1 ## gram ## =.001 ## kg . ## U=mgh=90 ## joules ## \approx 20 ## calories (1 calorie=4.184 joules). The answer is you can not even melt it with all of the available energy. You need ## 80 ## calories to completely melt it with 100% energy going into heating of the ice cube.

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Comeback City
Thanks for the help!

The cube passes through the atmosphere in dropping the 30000 ft, and can exchange heat with the surrounding atmospheric air, since its temperature is going to differ from that of the air. Do you know what the air temperature and density are at 30000 ft, and as a function of altitude? Do you know how to determine the heat transfer coefficient between the air an the object, at the terminal velocity of the object? This is all covered in courses in heat transfer and atmospheric science.

@Chestermiller Thank you. Yes, that is another part of the analysis that requires careful inspection. It can make a big difference if the atmosphere is at near freezing temperatures, or at temperatures in the ## T=20^o ## to ## 30^o ## C range.

@Chestermiller Thank you. Yes, that is another part of the analysis that requires careful inspection. It can make a big difference if the atmosphere is at near freezing temperatures, or at temperatures in the ## T=20^o ## to ## 30^o ## C range.
Actually, at 30000 ft (10 km, base of the stratosphere), the temperatures are on the order of -50 C.

Comeback City and Charles Link

## What is heat transferred to a falling object?

Heat transferred to a falling object is the amount of thermal energy that is transferred from the surrounding environment to an object as it falls. This transfer of heat can occur through various mechanisms such as conduction, convection, and radiation.

## How does heat transferred to a falling object affect its temperature?

The amount of heat transferred to a falling object can affect its temperature by either increasing or decreasing it. If the object is falling through a colder environment, the heat transfer will cause its temperature to decrease. On the other hand, if the object is falling through a warmer environment, the heat transfer will cause its temperature to increase.

## What factors influence the amount of heat transferred to a falling object?

The amount of heat transferred to a falling object is influenced by several factors such as the object's surface area, velocity, and the temperature difference between the object and its surrounding environment. Other factors may include the object's material and the medium through which it is falling.

## How is heat transferred to a falling object calculated?

The calculation of heat transferred to a falling object involves various equations and variables depending on the specific situation. In general, the equation for heat transfer is Q = mcΔT, where Q is the amount of heat transferred, m is the mass of the object, c is its specific heat capacity, and ΔT is the change in temperature.

## What are some real-world applications of understanding heat transferred to a falling object?

Understanding heat transferred to a falling object is crucial in various real-world applications such as designing parachutes, predicting the temperature of objects after re-entry from space, and studying the effects of heat transfer on falling bodies in industries such as manufacturing and construction. It is also essential in understanding the physics of meteorites and other objects falling from space.