Question

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

Answer 1

2401

Step-by-step 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.