T and V changing in an isobaric process

[BearY]

Homework Statement

Consider a 1000 to 700 hPa layer in the atmosphere that is at rest and is in hydrostatic balance. The layer is subjected to radiative cooling at a rate of 5.0e3 J/s/m2 for one hour.
a) Calculate the change in mean temperature for the layer assuming all energy goes into heating the layer. Hint: We derived the 1st law of thermodynamics on a per mass basis.
b) Find the resulting decrease in the thickness of the layer.

Homework Equations

$\Delta Q = \Delta U + W$
$\Delta p = -mg$
$\Delta T = \frac{\Delta U}{mC_p}$

The Attempt at a Solution

I am a bit confused and have a few questions.
What does "all energy goes into heating the layer" mean? From what I see, the energy goes in the layer is work done to the layer. Which is $p\Delta h$
Also, is radiative cooling $\Delta Q$, or $\Delta U$ only?
We can calculate the mass of a unit column since the layer is in hydrostatic balance.
Then the next step, from what I see, would depend on my understanding of the question.
Did I completely misunderstand the question?

 

[Andrew Mason]

Homework Statement

Consider a 1000 to 700 hPa layer in the atmosphere that is at rest and is in hydrostatic balance. The layer is subjected to radiative cooling at a rate of 5.0e3 J/s/m2 for one hour.
a) Calculate the change in mean temperature for the layer assuming all energy goes into heating the layer. Hint: We derived the 1st law of thermodynamics on a per mass basis.
b) Find the resulting decrease in the thickness of the layer.

Homework Equations

$\Delta Q = \Delta U + W$
$\Delta p = -mg$

Be careful with units. LS units are force/area. RS units are force. Δp = -(m/A)g where m/A is the mass per unit area of a column of air in the layer.

$\Delta T = \frac{\Delta U}{mC_p}$

The Attempt at a Solution

I am a bit confused and have a few questions.
What does "all energy goes into heating the layer" mean? From what I see, the energy goes in the layer is work done to the layer. Which is $p\Delta h$
Also, is radiative cooling $\Delta Q$, or $\Delta U$ only?

We can calculate the mass of a unit column since the layer is in hydrostatic balance.
Then the next step, from what I see, would depend on my understanding of the question.
Did I completely misunderstand the question?

The problem is not stated all that clearly. It appears to me that the radiative cooling relates to heat flow in the form of thermal radiation from the Earth surface. You are to assume that all this heat flow is captured by the layer (ie. Q = 5000 Js^-1m^-2)

AM