Question

A butane torch is a tool in which butane is burned to create a flame. A detector, located at 2meters from the flame, only measures the flux of green photons (λ=500[nm]). At a certain moment a detector measures a photon flux of ϕ(500nm)=3.37⋅10^25[s−1⋅m−2]. You may assume that the flame behaves like a black body and that the photon emission is isotropic. What is the temperature of the butane flame in?

Answer 1

given

R = 2 m

λ = 500 nm

ϕ = 3.37 x 10²⁵ s⁻¹ - m⁻²  

N / A t = ϕ = 3.37 x 10²⁵  

E / A t = N h C / A t λ

= ( N / A t ) ( h C / λ )

= T⁴

= 3.37 x 10²⁵ x 6.6 x 10^-34 x 3 x 10⁸ / 500 x 10^-9

= 5.67 x 10^-8 T

so the temperature of the butane flame is T = 3916.84 K