Consider a house that is approximated as a cube that is 8 m on a side and has no windows. The house loses heat from the four walls and the roof. For an inside temperature of $20 ^ { \circ } \mathrm { C }$ and an outside temperature of $- 20 ^ { \circ } \mathrm { C }$, it is desired to keep the total heat loss less than $5 \mathrm {~kW}$. What is the minimum $R$-value that is required for the walls and roof?

Question

Quizplus · Accepted Answer

The Answer is The total surface area is

5 imes ( 8 \mathrm {~m} imes 8 \mathrm {~m} ) = 320 \mathrm {~m} ^ { 2 }

Equation (8.5) gives the power loss as

P = A \Delta T / R

or

R = A \Delta T / P

So for

\Delta T = 40 ^ { \circ } \mathrm { C }

and

P = 5000 \mathrm {~W}

then the

R

-value is

R = \left( 320 \mathrm {~m} ^ { 2 } ight) imes \left( 40 ^ { \circ } \mathrm { C } ight) / ( 5000 \mathrm {~W} ) = 2.56 \mathrm {~m} ^ { 2 } \cdot { } ^ { \circ } \mathrm { C } / \mathrm { W }

Consider a House That Is Approximated as a Cube That 20∘C20 ^ { \circ } \mathrm { C }20∘C

Consider a House That Is Approximated as a Cube That $20 ^ { \circ } \mathrm { C }$