Chapter 14, Problem 40P

Two rooms, each a cube 4.0 m per side, share a 14-cm-thick brick wall. Because of a number of 100-W lightbulbs in one room, the air is at 30^DC, while in the other room it is at 10°C. How many of the 100-W bulbs are needed to maintain the temperature difference across the wall?

To determine

The number of 100W bulbs required to maintain the temperature difference across walls

Answer to Problem 40P

Solution:

20 bulbs

Explanation of Solution

Given Info:

The rooms are cubical and sides are 4m and thickness of wall is 14 cm. Air is at 30°C in one room and other is at 30°C.

Formula used:

Rate of heat flow can be calculated by

$\frac{Q}{t}=kA\frac{T_1-T_2}{l}$

Calculation:

$\frac{Q}{t}=kA\frac{T_1-T_2}{l}$

Substituting the values

$\begin{array}{l}=\frac{0.84J}{s.m.°C}(16m^2)\frac{(30-10)°C}{0.14m}\\ =1920W.\end{array}$

Number of bulbs, rounding off the power can be calculated as

$\frac{2000}{100}=20$