1. A physicist is constructing an expression for a new theory on the speed of the molecules of an ideal gas at temperature T that is dependent on (v) avg To assist he, compute and fully simplify (v ) avg using that, (1 4 ) avg = lov*f(v)dv, where v is speed and f(v) is the Maxwell-Boltzmann distribution given by, m my 2 f(v) = 4 (: 2 TCk T 21 2 KT . Compute the integral using that, 100 2ne - ax 1 . 3 . 5 ... (2n-1 ) dx = 2n+lan a2. Bobby Boucher, the waterboy for the University of Louisiana's Cougars football team, fills a large orange insulated plastic water tank with 17.0L of high quality H,O that is initially at a temperature of T,, = 20.0 C, the same temperature of the ambient air around the football field. If he adds 3.00kg of ice at an initial temperature of T; = 0.00 . C, a) find the equilibrium temperature of the water in the tank. You may assume that all of the ice melts, and that the tank does not absorb or transmit heat, and therefore thermally isolates the ice water from the surrounding air. b) find the change in entropy due to the thermodynamic process of the ice and water reaching an equilibrium temperature. Note that the phase change is indeed part of this process. c) if Mama comes to the field and gets angry because foosball is for the devil and dumps the cold water onto the ground, causing it to reach thermal equilibrium with the air, find the change in entropy to the air assuming that the temperature of the air remains unchanged. d) find the total change in entropy to the universe due to the processes outlined in parts b & c