A sample question for a test

The Sun has an effective temperature of Ts = 5800 K, while the star 40 Eridani has an effective temperature of Te = 5100 K. Treat both as perfect blackbodies.

1. At what wavelength will the Sun produce the peak specific intensity?
2. Consider one square meter of each star's photosphere. The Sun will produce more power -- integrated over all wavelengths -- from this one square meter than will 40 Eridani. What is the ratio of

   
                   Power emitted by 1 sq. m. of the Sun
                 -----------------------------------------
                   Power emitted by 1 sq. m. of 40 Eridani
        

3. But in real life, the total power emitted at all wavelengths by the Sun exceeds that emitted at all wavelengths by 40 Eridani by a factor of 2.88. Explain quantitatively the physical reason for this difference.

It's possible there might be a bonus section added to one question for a small additional credit (+10% or +15%), like this:

Bonus!

4. The absolute bolometric magnitude of the Sun is 4.83. What is the absolute bolometric magnitude of 40 Eridani?