4. A tube of 1m length is open at one end and is filled with a stoichiometric CH4/ air mixture. The temperature distribution in the unreacted gas (T1) is as shown in the figure. At time zero the mixture is sparked at the open end and a flame propagates down the tube. The open end allows the pressure to stay at one atmosphere and keeps the laboratory coordinate velocity of the unreacted gas at zero. When the temperature of the unreacted gas is 300K, SL=0.37m/s. This will increase as the unreacted gas temperature increases according to Equation 4.27 (p. 159) where E/R=24,538 K. Furthermore, note that Tf=2200K ( Tf is the final product gas temperature) when T1=300K, but due to disassociation, Tf=0.5T1 as discussed on p. 159 . Make use of this information to find the time needed for the flame to reach the end of the tube. (Note that the practical application of this problem is that of a flame passing across an engine cylinder. Here, the propagation of the enclosed flame leads to a pressure and temperature increase due to the isentropic compression of the unburned gas. The flame speed is not strongly influenced by the pressure, but it is by the temperature. The real process is more complex because (1) the unreacted gas temperature ahead of the flame must be calculated on the fly, and (2) there will be a non-zero velocity in the unreacted gas due to the compression.)