Question

a cubical box 20-cm on a side is contructed from 1.2 cm thick concrete panels. A 100-W light bulb is sealed inside the box. What is the temperature on teh inside ofthe box when the light is on and the outside temperature is 20C

Answer 1

Temperature on the inside ofthe box

Step-by-step explanation:

The power of the light bulb is the rate of heat conduction of the bulb,
`dq/dt = 100 W`

The thickness of the wall, L = 1.2 cm = 0.012m

Length of the cube's side, x = 20cm = 0.2 m

The area of the cubical box, A = 6x²

A = 6 * 0.2² = 6 * 0.04

A = 0.24 m²

Temperature of the surrounding,
`T_0 = 20^0 C = 273 + 20 = 293 K`

Temperature of the inside of the box,
`T_(in) = ?`

Coefficient of thermal conductivity, k = 0.8 W/m-K

The formula for the rate of heat conduction is given by:

`dq/dt = (kA(T_(in) - T_0))/(L) \\\\100 = (0.8*0.24(T_(in) - 293))/(0.012)\\\\T_(in) - 293 = (100 * 0.012)/(0.8*0.24) \\\\T_(in) - 293 = 6.25\\\\T_(in) = 293 + 6.25\\\\T_(in) = 299.25 K\\\\T_(in) = 299.25 - 273\\\\T_(in) = 26.25^0 C`