Write the code in Colab to solve this problem! Exercise 6.18: The temperature of a light bulb An incandescent light bulb is a simple device-It contains a filament, usually made of tungsten, heated by the flow of electricity until it becomes hot enough to radiate thermally. Essentially all of the power consumed by such a bulb is radiated as elec- tromagnetic energy, but some of the radiation is not in the visible wavelengths, which means it is useless for lighting purposes. Let us define the efficiency of a light bulb to be the fraction of the radiated energy that falls in the visible band. It's a good approximation to assume that the radiation from a filament at temperature T obeys the Planck radiation law (previously encoun- tered in Exercise 6.13 on page 267), meaning that the power radiated per unit wave- length obeys 4-5 (A) = 27 Ahe? eh/MT-1' where A is the surface area of the filament, h is Planck's constant, c is the speed of light, and ky is Boltzmann's constant. The visible wavelengths run from is = 390 nm to 12 = 750nm, so the total energy radiated in the visible window is 1(x) dx and the total energy at all wavelengths is S() dl. Dividing one expression by the other and substituting for I(A) from above, we get an expression for the efficiency of the light bulb thus: 1-5/(eht/WT - 1) 1 So* 1-57(ek/AkT - 1) where the leading constants and the area A have canceled out. Making the substitution x = hc/AkyT, this can also be written as //AKT x/et - 1) dx 15 thc / A4 kgr x dx, S * /(e' - 1) dx where we have made use of the known exact value of the integral in the denominator. a) Write a Python function that takes a temperature T as its argument and calcu- lates the value of n for that temperature from the formula above. The integral in the formula cannot be done analytically, but you can do it numerically using any method of your choice. (For instance, Gaussian quadrature with 100 sample points works fine.) Use your function to make a graph of n as a function of tem- perature between 300 K and 10 000 K. You should see that there is an intermediate temperature where the efficiency is a maximum. 1 = Azket er-1 289 CHAPTER 6 | SOLUTION OF LINEAR AND NONLINEAR EQUATIONS b) Calculate the temperature of maximum efficiency of the light bulb to within 1K using golden ratio search. (Hint: An accuracy of 1K is the equivalent of a few parts in ten thousand in this case. To get this kind of accuracy in your calculation you'll need to use values for the fundamental constants that are suitably accurate, i.e., you will need values accurate to several significant figures.) c) Is it practical to run a tungsten-filament light bulb at the temperature you found? If not, why not