Interior temperature of a solar collector

[imatreyu]

Homework Statement

A solar collector has an effective collecting area of 12 m^2. The collector is thermally insulated, and so conduction is negligible in comparison with radiation. On a cold but sunny winter's day the temperature outside is -20.0 C, and the Sun irradiates the collector with a power per unit area of 300 W/m^2. Treating the collector as a black body (i.e., emissivity = 1.0), determine its interior temperature after the collector has achieved a steady-state condition (radiating energy as fast as it is received).

Homework Equations

I used P = s A e (T^4 - To^4)

The Attempt at a Solution

300 = (5.66 x 10^-8)(12)(T^4 - 253.15^4)


The answer should be 38 C, according to the book, but I don't get that at all when I solve for T. . .I keep getting -13 C. What am I doing wrong?

 

[gneill]

I used P = s A e (T^4 - To^4)

The Attempt at a Solution

300 = (5.66 x 10^-8)(12)(T^4 - 253.15^4)


The answer should be 38 C, according to the book, but I don't get that at all when I solve for T. . .I keep getting -13 C. What am I doing wrong?

The numbers look okay. When I solve the equation for T and plug in the given numbers I get 38.2 C. Must be a finger issue.

 

[imatreyu]

Darn. .. I keep getting -13. Maybe I need to review basic order of operations. . .

 

[imatreyu]

Oh! Why do I ignore the area?