Temperature(thermal radiation transfer)

[Ajwrighter]

1. A solid cylinder of radius r1 = 2.3 cm, length h1 = 4.2 cm, emissivity 0.88, and temperature 24°C is suspended in an environment of temperature 55°C. (a) What is the cylinder's net thermal radiation transfer rate P1? (b) If the cylinder is stretched until its radius is r2 = 0.52 cm, its net thermal radiation transfer rate becomes P2. What is the ratio P2/P1?
2. P1 = (\sigma) (\epsilon) A1(T_env⁴ - T⁴)

A1 = 2(\pi) r1² + 2 (\pi) r h
3. A1 = 9.393362*10^-3m²
P1 = (5.67*10^-8)(.88)(9.393362*10^-3)((273+55)⁴-(273+24)⁴)) = 1.77WI have (b) .. but for some reason (a) is wrong.. here is answer for (b) \frac{P2}{P1} = 2.87
.

 

[Ajwrighter]

Ok I just did it in mathmatica .. and it gave the same answer .. If
my intuition is incorrect then the only possible solution would be
that P1 is somehow =(\sigma) (\epsilon) A1((24+273)⁴) ... but that's not how the question reads

 

[Ajwrighter]

I asked a friend he agrees with me.. but are we both wrong? not sure why the answer is considered wrong

 

[Ajwrighter]

had another person agree.. anyway I could get someone to review this problem and confirm?

 

[Ajwrighter]

any attempts?

 

[Ajwrighter]

ok I've resolved the problem. Both the book, and their online website have two distinct wrong equations to use.. The correct one would involve flipping the Tenv^4 with the T^4.. so it would read (T^4 - Tenv^4). So, I dub this problem as resolved in case anyone was interested.