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Created with Fabric.js 1.4.5 BOILING WATER How long does it take to boil the water? METHODOLOGY The differential equation taken for consideration is, dT/dt = k(T-T_m)This differential equation refers to the rate of temperature against time taken for water to boil. 1. 2. Based on the following assumptions: - k: Is a value constant- T: Temperature of boiling water in Fahrenheit (degree F)- T_m: Temperature of the surroundings in Fahrenheit (degree F)- T(0): Initial temperature of water at time, t = 0 minutes- T(5): Temperature of water at time, t = 5 minutes- T(t): Temperature of water at an unknown time, t Where the assumed values are: - T_m = 76 degress F- T(0) = 96.8 degrees F- T(5) = 150 degrees F- T(t) = 212 degrees F SOLUTION 1. 2. 3. 4. CONCLUSION 3. Equation 1 is differentiated to obtain a general equation of temperature,T at time, t for boiling water. 4. Assumed values for T=76 at t=0 is substituted to obtain unknown constant C. Value of C is used in the equation of T=150 at t=5to obtain constant k. 5. 6. All unknown values are used tosolve t at T where T(t) = 212 degree F. In a nutshell, the time taken for water to boil was determined by using the rate of temperature against time equation. A separable method was used toapproach the differential equationand values used was obtained throughassumption. Solving the equation usingassumed values, time taken obtained forwater to boil is, 7.4 minutes.
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