Radiational Cooling: Calculate Net Heat Loss

[tebowgocray]

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.

 

[Bystander]

"Latent heat value"? You mean C_P? What value? "pda"? Check your units.