A heated filament of a bulb is radiating maximum energy at wavelength `3.14 xx 10^(-5) ` cm. Determine the total amount of energy lost per second per unit area by the filament if the temperature of the surrounding air is `20^@C` . Take,
`b = 0.288 cm K`
`sigma = 5.77 xx 10^(-5) erg s^(-1) cm^(-2) K^(-4)`

Explanation

To solve the problem step by step, we will use the concepts of Wien's Law and Stefan-Boltzmann Law.

### Step 1: Calculate the Temperature of the Filament
Using Wien's Law, we can find the temperature of the filament. Wien's Law states that the temperature (T) of a black body is inversely proportional to the wavelength (λ) at which it emits maximum radiation.

The formula is given by:
\[ T = \frac{b}{\lambda} \]

...