How to cook the perfect egg 4 points As an egg cooks, the proteins first denature and then coagulate. When the temperature exceeds a critical point, reactions begin and proceed faster as the temperature increases. In the egg white, the proteins start to coagulate for temperatures above 63 C while in the yolk the proteins start to coagulate for temperatures above 70 C. For a soft-boiled egg, the white needs to have been heated long enough to coagulate at a temperature above 63 C, but the yolk should not be heated above 70C. For a hard-boiled egg, the center of the yolk should be allowed to reach 70 C. The following formula expresses the time it takes (in seconds) for the center of the yolk to reach the temperature Ty (in degrees centigrade) To- Tw Ty-T n 0.760 Ka24/3) Here, M, p, c, and K are properties of the egg: M is the mass, is the density, c is the specific heat capacity, and K is the thermal conductivity. Relevant values are M-47 g for a small egg and M-67 g for a large egg:-1.038 g . cm-3-3.7 J . g-1. K-1 and K = 5.4 . 10-3w . cm-1-K-1 Furthermore, Twis the temperature (in degrees centgrade) of the boiling water, and To is the original temperature (in degrees centigrade) of the egg before being put in the water We wish to implement this formula, but first, let's define some intermediate terms to make things easier to program To- Tw Ty-Ty Now the formula can be expressed as tIni Implement the formula in a program, set Tw= 100C and Ty = 70 Compute t for a large egg taken from the fridge (To=4C) in variable t-large-fridge o o Compute t for a large egg starting at room temperature (To 20 C) in variable t_large_room Your submission should include at least two parts 1. t_large_fridge 2. t_large_room math.log provides the natural logarithm function. You should use the library value of pi as well