Question

At high noon, the sun delivers 1 000 W to each square meter of a blacktop road.

What is the equilibrium temperature of the hot asphalt, assuming its emissivity e = 1? (σ = 5.67 × 10−8W/m2⋅K4) .

a. 75°Cb. 84°Cc. 91°Cd. 99°C

Answer 1

The correct answer is c, T = 91.3°C

Step-by-step explanation:

For this exercise let's use Stefan's equation on the emission of a black body

P = σ A e T⁴

Where σ is the Stefan-Boltzmann constant, A the area, and 'e' emissivity and T the absolute temperature

In this case give the absorbed power is 1000W per square meter, let's clear the temperature equation

T⁴ = (P / A) 1/σ e

Let's calculate

T⁴ = 1000 1 / (5.67 10⁻⁸ 1)

T⁴ = 176.37 10⁸

T =
`\sqrt[4]{176.37   10^8}`

T = 3.6442 10² K

Let's reduce to degrees Celsius

T = 364.42 -273.15

T = 91.3 ° C

The correct answer is c