Question

Section I: First Order Systems 1) A microwave oven is used to heat a cylindrical glass beaker completely full of water. The magnetron tube generates 800 watts of thermal power, all of which is absorbed by the water. The glass beaker sits on a thermally insulated plate. As the microwaves increase the temperature of the water, the beaker temperature will also increase due to conduction and convection from the Mode Stirrer Wave Guide Magnetron Tube (source of radiation) Oven Cavity Filter Step-up Transformer Power Plug water. Assume the water temperature changes uniformly throughout. Ignore any small amounts of thermal energy lost to the air or any other part of the microwave oven. The initial water temperature is 20° C and its specific heat is 4186 J/( kg °C) ID 150 mm The beaker has a density of 2.23 g/cm3 and has a specific heat of 750 J/ (kg C). The sidewall dimensions of the beaker are shown to the left. The top is open, and the bottom is the same thickness as the sidewalls. The initial beaker temperature is 20° C The water to beaker heat transfer coefficient is 300 W/(m2 °C) Water depth 110 mm If the internal beaker conduction is much faster than the conduction at the water/beaker interface, make an estimate of the temperature of the beaker if the heat lost to the beaker is considered small as compared to the water's heat input by the magnetron tube. a) after 10 seconds b) after 4 minutes OD 160 mm

Answer 1

Here the aoa uneofprenemts thesh T 20 C = 4186 3 223o E2-23 = 30D W =I942 x 10 4 m2 -1-0-15) Brcken S.086 x 1-4 Tx015x 0. X Beaker cs Scanned with CamScanner

At fisat, emergy halamce for alexaflex Wat (-20) 800 x10 /.94 2 x t0 *3 x 418 6 x O 20.984 C Nou heat isamofer from lar aker uales t h frakes CBT,- 20) = Aakes 7 -7) (Tfo-20)- 300x 6.947 x (20-14 20.15C CS Scanned with CamScanner

me alance foWales af les 4 minule TVwalx 4186x C-2 -3. 000 X I942 x 10 8o0 x 4 x 6o 2 0 = 43- 618 °c T Now heat nPes om wales to the leaker, T - 20 Beakes X - 20 2. 2 30 X 8 .08 x 10 tx o-2 (43-118 - 2) I07 35 C CS Scanned with CamScanner