Question

If the temperature of an object is multiplied by 7 , the amount of power radiated is multiplied by what number?

Answer 1

Answer:

2401

Explanation:

The amount of power radiated  by an object can be calculated with the Stefan-Boltzmann law, this law is expressed as:

$\frac{\textrm{P}}{\textrm{A}}=e*\sigma*T^{4}$

• P = total power radiated.
• A = surface area.
• $e$ = emissivity.
• $\sigma$ = Stefan-Boltzmann constant.
• T =  temperature of the object  (in degrees Kelvin).

In this problem, it's supposed that we move from state 1

($\textrm{P}_{1}=\textrm{A}_{1}*e_{1}*\sigma_{1}*(T_{1})^{4}$)

where all the variables are known, to state 2, where $\textrm{A}_{1} = \textrm{A}_{2}$, $e_{1}=e_{2}$, $\sigma_{1}=\sigma_{2}$, and T is 7 times bigger than before, so to find $\textrm{P}_{2}$ we have the replace $\textrm{T}_{2} =7*\textrm{T}_{1}$.

$\textrm{P}_{2}=\textrm{A}_{2}*e_{2}*\sigma_{2}*(T_{2})^{4} \\\textrm{P}_{2}=\textrm{A}_{1}*e_{1}*\sigma_{1}*(7*T_{1})^{4} \\\textrm{P}_{2}=\textrm{A}_{1}*e_{1}*\sigma_{1}*(T_{1})^{4}*7^{4} \\\\ \textrm{P}_{2}=\textrm{P}_{1}*2401$

This means that the amount of power radiated is multiplied by 2401.