Q. 1.58 - An Introduction to Thermal Physics

Question

According to a standard reference table, the R value of a 3.5 inch-thick vertical air space (within a wall) is 1.0 R in English units), while the R value of a 3.5-inch thickness of fiberglass batting is 10.9. Calculate the R value of a 3.5-inch thickness of still air, then discuss whether these two numbers are reasonable. (Hint: These reference values include the effects of convection.)

Step-by-Step Solution

Answer

The  value of 3.5 inch thickness of still air is R_air= 0.176 m². ^oK.s.J^-1 

Step 1: To Calculate R

$R$ value  is,

$R=\frac{\Delta k}{k_t}$

For

$\text{ air }{k}_t=0.026{\mathrm{Wm}}^{-1}{k}^{-1}$

So,

$3.5 inch=3.5\times 25.6mm$

$=89.6\times {10}^{-3} \mathrm{m}$

$R_{\text{air }}=\frac{89.6\times {10}^{-3} \mathrm{m}}{0.026{\mathrm{Wm}}^{-1}{ \mathrm{K}}^{-1}}$

$=3.45{\omega }^{-1}{ \mathrm{m}}^{2}k$

Step 2: After conversion.

Then,

$R_{\text{air }}=\frac{3.45}{0.58}$ $of ft{ }^2 hr/btu$

$R_{air}=5.95$ $of ft{ }^2 hr/btu$

As a result, the value does not match the reference value $(f=1)$.

Because of the convection process, reference values incorporate the impacts of convection.

The air's thermal conductivity rises.

As a result, the value of $R$ decreases.