Which of the following graphs correctly represents the relation between ln(E) and ln(T) , where E is the amount of radiation emitted per unit time from a unit area of the body and T is the absolute temperature?

Question

Which of the following graphs correctly represents the relation between ln(E) and ln(T) , where E is the amount of radiation emitted per unit time from a unit area of the body and T is the absolute temperature? (A) Option 1

(B)

(C)

(D)

Tardigrade Admin · Accepted Answer

We know, E=ϵ σ T4 ⇒ ln E=ln⁡ϵ σ +4ln⁡T εσ < 1 , hence, lnϵ σ is negative. <img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-cye9akuenf4y.png" />

Q. Which of the following graphs correctly represents the relation between $l n (E)$ and $l n (T)$ , where $E$ is the amount of radiation emitted per unit time from a unit area of the body and $T$ is the absolute temperature?

We know,
$E = ϵ σ T^{4}$
$\Rightarrow l n E = l n ϵ σ + 4 l n T$
$ε σ < 1$ , hence, $l n ϵ σ$ is negative.

Q. Which of the following graphs correctly represents the relation between ln(E) and ln(T) , where E is the amount of radiation emitted per unit time from a unit area of the body and T is the absolute temperature?

We know, E=ϵσT4 ⇒lnE=ln⁡ϵσ+4ln⁡T εσ<1 , hence, lnϵσ is negative.

Q. Which of the following graphs correctly represents the relation between $l n (E)$ and $l n (T)$ , where $E$ is the amount of radiation emitted per unit time from a unit area of the body and $T$ is the absolute temperature?

We know,
$E = ϵ σ T^{4}$
$\Rightarrow l n E = l n ϵ σ + 4 l n T$
$ε σ < 1$ , hence, $l n ϵ σ$ is negative.