Question

An electric current passes through a metal strip 0.40 cm by 5.9 cm by 0.14 mm, heating it at the rate of 52 W. The strip has emissivity e = 1.0 and its surroundings are at 340 K. What will be the temperature of the strip if it's enclosed in (a) a vacuum bottle transparent to all radiation and (b) an insulating box with thermal resistance R = 7.5 K/W that blocks all radiation? Express your answer using two significant figures. Express your answer using two significant figures.

Answer 1

A = area = 2 (0.40 x 5.9 x 10^-4 + 5.9 x 0.14 x 10^-5 + 0.14 x 0.40 x 10^-5) = 0.00048 m²

P = 52 W

T₁ = ?

T₂ = 340 K

using the equation

P = $\sigma$Ae (T₁⁴ - T₂⁴)

52 = (5.67 x 10^-8) (0.00048) (1) (T₁⁴ - (340)⁴)

T₁ = 1177.75 K

b)

R = 7.5 k/W

using the equation

P = - (T₂ - T₁) /R

52 = - (340 - T₁) /(7.5)

T₁ = 730 K