please show step by step solution

3. A solid slab of material of mass, M, is being heated by an electric heater at a rate of Ort), where the temperature in the slab (T (t) in C) is assumed to be uniform. The slab loses heat to the surroundings, which is at a temperature of T. (in C) and is considered constant. The temperature of a slab is described by the following dynamic balance: dTt) dt Q -a [T* - T1 where, Qct) is the rate of heat input in kW (kJ/s), C-6 kJ/(kg) is the heat capacity of the slab, M-0.5 kg, T.-300C (constant), and a 5 x 100 kWC. At the initial steady T = 400 C and 7 = 8.75 kW. a) Obtain the transfer function (in deviation variables) G(s), relating the temperature of the slab (T'(s)) to the rate of heat input (Q'(s)). Leave the function in terms of the variables in the problem statement, G(s) T(S) Q (8) b) Write the value of the gain and time constant of the transfer function (with units). K-7.81 C/kW 1-23.4 sec c) The temperature in the slab needs to be reduced to a new steady state of 390C by changing o(t) in a stepwise fashion. What is the new value of Qas estimated from the linearized model? Q-7.47 kW