Two identical spheres A and B are suspended in an air chamber which is maintained at a temperature of `50^@C`. Find the ratio of the heat lost per second from the surface of the spheres if
a. A and B are at temperatures `60^@C` and `55^@C`, respectively.
b. A and B are at temperatures `250^@C` and `200^@C`, respectively.

Explanation

To solve the problem, we will use Stefan-Boltzmann's law, which states that the power radiated by a black body per unit area is proportional to the fourth power of its absolute temperature. The formula for the heat lost per second from the surface of a body is given by:

\[ E = \epsilon \sigma (T^4 - T_0^4) \]

where:
- \( E \) is the heat lost per second,
- \( \epsilon \) is the emissivity (which is the same for both spheres),
- \( \sigma \) is the Stefan-Boltzmann constant (which is also the same for both spheres),
...