What is the heat flow through the ceiling into the attic in 4.5h?

[tquiva]

Homework Statement

The ceiling of a room has an area of 135ft^2. The ceiling is insulated to an R value of 30 (in units of ft^2*deg. F*h/Btu). The surface in the room is maintained at 63 deg. F, and the surface in the attic has a temperature of 38 deg. F. What is the heat flow through the ceiling into the attic in 4.5 h?
Express your answer in (a) BTU and (b) joules.

Homework Equations

The equation I used was the heat current equation with thermal resistance.
H = [A(Th-Tc)] / R

The Attempt at a Solution

The equation I used was the heat current equation with thermal resistance.
H = [A(Th-Tc)] / R
= [(135ft^2)(63 deg. F - 38 deg. F)] / [30 ft^2*deg. F*h/BTU]
= [(135)(25)] / [30]
= 3.8 BTH / h

I've already made an attempt to this problems and my results don't seem to not be right. Can someone please help me?

 

[kuruman]

135*25/30 is not 3.8.

 

[kerimek]

Based on the given information, the heat flow through the ceiling into the attic in 4.5 hours can be calculated using the heat current equation with thermal resistance. Using the given values, we can plug them into the equation and solve for the heat flow (H).

H = [A(Th-Tc)] / R
= [(135ft^2)(63 deg. F - 38 deg. F)] / [30 ft^2*deg. F*h/BTU]
= [(135)(25)] / [30]
= 3.8 BTU / h

Therefore, the heat flow through the ceiling into the attic in 4.5 hours is 3.8 BTU. To convert this into joules, we can use the conversion factor 1 BTU = 1055.06 joules.

(a) In BTU: 3.8 BTU
(b) In joules: 3.8 BTU x 1055.06 joules/BTU = 4010.4 joules

Therefore, the heat flow through the ceiling into the attic in 4.5 hours is 3.8 BTU or 4010.4 joules. It's important to note that this is the heat flow in 4.5 hours, so if you want to find the total heat flow over a longer period of time, you would need to multiply this value by the total time.