Verified answer

I think you need to apply Fourier's Law, which gives the "heat flow rate" across a homogeneous material between two endpoints, each of which is at a constant temperature (see Source 1):

(1) ΔQ / Δt = - κ * A * ΔT / Δx,

where:

ΔQ / Δt = heat flow rate in W (to be calculated)

κ = thermal conductivity in W / m·◦C = 0.8 (given)

A = surface area = 4320 cm^2 (given) in m^2

ΔT = the difference in temperature between the two endpoints = Tto - Tfrom in C

Δx = the distance between the two endpoints = the thickness of the glass = 3.6 mm in m

Now, simply convert the given values to their proper units as indicated, plug them into equation (1), which will give watts, and divide by 1000 to get kW. Pay attention to the signs, as the flow rates in (a) and (b) are in opposite directions.

Converting the values given where necessary:

(2) A = 4320 cm^2 = 0.432m^2

(3) ΔT = Tin - Tout = (73 - 94)F = (5/9) * (73 - 94) C = -11.7C

(4) Δx = 3.6 mm = 3.6e-3m

Substituting in (1):

(5) ΔQ / Δt = - 0.8 * 0.432 * (-11.7 / 3.6e-3)

= 1123.2W or

= 1.12kW is the energy transfer by conduction---part (a), positive from outside to inside

For part (b) we have a different temperature difference, so we need to modify (3):

(6) ΔT = Tin - Tout = (73 - 0)F = (5/9) * (73 - 0) C = 40.6C

Notice the difference in sign. Recalculating,

(7) ΔQ / Δt = - 0.8 * 0.432 * (40.6 / 3.6e-3)

= -3897.6W or in kW and rounding,

= -3.90kW is the energy transfer by conduction---part (b), negative from outside to inside, therefore the (positive) flow is from inside to outside, as you would expect.

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