Thermodynamics - heat transfer

[urgent]

Homework Statement

if the temperature of an object changes from 80 to 433 degrees Celsius, but the area and emissivity remains constant, by how much does radiated power increase?

Homework Equations

P=phi*A*e*T^4

The Attempt at a Solution

i tried to do this:
80^4-433^4. and get the temperature change...but i do not know where to go from here, please if someone could give good explanation about this, i got an exam in 2 days=/..thanks!=]

 

[rock.freak667]

So the change is E=εA(T₂⁴-T₁⁴) (remember to change the temperatures to Kelvin).

Originally the power was E=εAT₁⁴

So what is the ratio of the change in power to the original power?

 

[urgent]

so i did this:
706^4 - 353^4
=2.329*10^11
um now how do i find the ratio of the change from this?

 

[rock.freak667]

so i did this:
706^4 - 353^4
=2.329*10^11
um now how do i find the ratio of the change from this?

So you have ΔE= εA(2.239x10¹¹)

Initially E = εAT₁⁴

So get E and just find ΔE/E

 

[rwisz]

As the temperature of an object increases, the amount of heat energy it radiates also increases. This is described by the Stefan-Boltzmann law, which states that the power radiated by an object is proportional to the fourth power of its absolute temperature (in Kelvin) and its surface area and emissivity (which is assumed to be constant in this problem).

Using the equation you provided, we can calculate the radiated power at the initial temperature of 80 degrees Celsius (353 Kelvin) and the final temperature of 433 degrees Celsius (706 Kelvin).

P1 = phi * A * e * T1^4 = phi * A * e * (353)^4
P2 = phi * A * e * T2^4 = phi * A * e * (706)^4

To find the increase in radiated power, we can subtract P1 from P2:

P2 - P1 = phi * A * e * (706)^4 - phi * A * e * (353)^4

= phi * A * e * (706^4 - 353^4)

= phi * A * e * (1.192 x 10^14 - 4.45 x 10^11)

= phi * A * e * 1.192 x 10^14

Therefore, the radiated power increases by approximately 1.192 x 10^14 times when the temperature increases from 80 to 433 degrees Celsius. This shows the significant impact that temperature has on heat transfer through radiation.