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?

 

[rwisz]

I would first double check my calculations and make sure all units are consistent. It is possible that a small error in unit conversion or a mistake in the algebra could lead to a different answer. Additionally, I would make sure the assumptions made in the problem (such as neglecting conduction and treating the collector as a black body) are appropriate and do not affect the final result significantly. If the calculations and assumptions are correct, I would try to understand why the answer in the book is different and potentially reach out to the author or other experts in the field for clarification. It is also important to note that this is a simplified model and in reality, the interior temperature of a solar collector may be affected by other factors such as wind, humidity, and heat loss from the surrounding environment.