Question

By solving this exercise, you will answer to the following questions: How hot is hell? > When will hell freeze over? In order to help you a bit in solving this problem, I am going to give you some information that will simplify the solution process. As such, we are going to base the problem on a few assumptions: We will assume that hell does actually exist and it obeys to the laws of Nature as we know them (there are the two biggest assumptions!). Earth's population is increasing, in first approximation, exponentially, we will assume that the number of souls in hell follows the same trend. In mathematical language, and indicating with n the number of moles of souls in hell, we have that where both A and a are positive constants, and t indicates time. We will also assume that at the initial condition (tO, corresponding to, let's say, 5,000 years ago), only one soul was present in hell (the Devi's sou). From the previous formula, we immediately write that mol 022 x 1033 mol1.66x10 We will also assume that souls entering in hell will not leave. We will treat the souls in hell as an ideal gas. We will assume that the pressure of hell is 1 atm, as on earth (you can easily repeat the problem by imposing a very high or a very low value for the pressure according to your believes about the location of hell with respect to Earth). . . a) Determine the value of the constant a, by considering that roughly 100 people have been populated Earth since the Devil was thrown to hell, and that 10% of them have entered hell. (15 points) b) Since at t0 only one soul was present in hell, we will assume that hell's volume corresponded back there to the average volume of a house (o 2,000 t? x 8-ft). As the number of souls in hellis increasing exponentially, we can declare that this is also true for volume of hell; that is:

The answer to a = 0.004144... please continue at b

Answer 1