Consider a system of N tanks that are connected in series, as shown in the figure below. Each tank initially contains V=1m3 of watec, which Is fully mixed, and has two inlet streams and two outlet streams. Water at temperature TR,i enters tank 1 at a volumetric flow rate VRpha, and For the questions below, you can consider that the flows are such that the liquil volume in each of the tanks remains constant. Assume that water has a density =1000kgm3 and heat capacity C=4.2kJkg1. Note that for each of the matrices the set of differential equations that need to be solved can be written in matrix form as dtdT=AT+b This is a system of inhomogenous differential equations. This follows a similar procedure to solve homogenous differential equations, with the addition that the inhomogenous b term must be multiplied by P1 too. 1. Consider the case where VR,in=VR,out=0.1m3s1,VL,ln=VL,out=0,v^R=0.2m3s1,TR,hn=80C, and vL=0.1m3s1. In the case of 3 tanks, if the initial temperature of tank 2 is 80C and the initial temperature of the other tanks is 10C, solve the differential equations and plot the varlation of the temperature of each tank with time. 2. Consider the case where VR,m=VL,la=VR,out=VL,aat=0.1m3s1,v^R=v^L=0.1m3s1,TR,a=80C, and TL,in=10C. In the case of 3 tanks, if the inltial temperature of the water in all of the tanks is 60C, solve the differential equations and plot the variation of the temperature of each tank with time