Radiational Cooling: Calculate Net Heat Loss

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In summary, on a clear night, the loss of infrared radiation to space causes a 10 m layer of the atmosphere to cool by 5 K over 10 hours. Using a density of 1.25 kg^-3 for air, the net rate of heat loss by radiational cooling is 1.74 W m^-2. The first law of thermodynamics is used, with dq = du + pda, but since the area is fixed, the second term is eliminated. This leaves dq = du, and since we are looking for the net rate of heat loss, it is given by the change in heat over the change in time, or dq/dt = Cp(dT/dt). However, attempting to multiply the
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Homework Statement


On a clear night, the loss of infrared radiation to space causes the loses 10 m of the atmosphere to cool by 5 K over 10 Hrs. Assuming a density of 1.25 kg^-3 for the air, what is the net rate of heat loss by radiational cooling, in Wm^-2 (Answer: 1.74 W m^-2)

Homework Equations


I know the first law of thermodynamics plays a role: dq = du + pda

The Attempt at a Solution


I believe the area is fixed so it will eliminate the second term leaving dq = du and du = CpdT leaving dq = CpdT. Since the net rate of heat loss is what we are looking for, it would be a change in hear over a change in time. So I have:

Cp(dT/dt) = dq/dt

then I tried to multiply the latent heat value by the (dT/dt) value to get dq but it did not provide the correct answer.
 
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"Latent heat value"? You mean CP? What value? "pda"? Check your units.
 

What is radiational cooling?

Radiational cooling is a process in which an object loses heat through the emission of thermal radiation. This can occur when the temperature of the object is higher than the surrounding air or when the object is exposed to a clear night sky.

How is net heat loss calculated?

Net heat loss is calculated by taking into account the amount of thermal radiation emitted by an object and the amount of thermal radiation absorbed from the surrounding environment. This can be calculated using the Stefan-Boltzmann law, which states that the rate of thermal radiation emitted by an object is proportional to the fourth power of its absolute temperature.

What factors affect radiational cooling?

The rate of radiational cooling is affected by several factors, including the temperature difference between the object and its surroundings, the object's surface area, and the presence of any insulating materials.

How does radiational cooling impact the environment?

Radiational cooling plays a significant role in regulating the Earth's temperature. It is responsible for the formation of dew and frost, and it also helps to cool the Earth's surface during clear nights.

What are some applications of radiational cooling?

Radiational cooling has various applications, including refrigeration, air conditioning, and the cooling of electronic devices. It is also commonly used in agricultural practices such as protecting crops from frost damage.

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