Question Solved1 Answer Problem begins here: An object at an unknown temperature is placed in a room which is held at a constant temperature of 30 F. If after 10 minutes the temperature of the object is 0 F and after 20 minutes the temperature of the body is 15 F what is the initial temperature of the object? Assume Newton's Law of Cooling which states that the rate of change of the temperature of a body is proportional to the temperature difference between the body and its surrounding medium. Choose the correct answer from among the given choices. -55 F -30 F (c) -14 F D) -12 F O F (F) 45 F G) 68 F The problem is unsolvable as it lacks additional information.

GYBRDT The Asker · Physics
Transcribed Image Text: Problem begins here: An object at an unknown temperature is placed in a room which is held at a constant temperature of 30 F. If after 10 minutes the temperature of the object is 0 F and after 20 minutes the temperature of the body is 15 F what is the initial temperature of the object? Assume Newton's Law of Cooling which states that the rate of change of the temperature of a body is proportional to the temperature difference between the body and its surrounding medium. Choose the correct answer from among the given choices. -55 F -30 F (c) -14 F D) -12 F O F (F) 45 F G) 68 F The problem is unsolvable as it lacks additional information.
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Transcribed Image Text: Problem begins here: An object at an unknown temperature is placed in a room which is held at a constant temperature of 30 F. If after 10 minutes the temperature of the object is 0 F and after 20 minutes the temperature of the body is 15 F what is the initial temperature of the object? Assume Newton's Law of Cooling which states that the rate of change of the temperature of a body is proportional to the temperature difference between the body and its surrounding medium. Choose the correct answer from among the given choices. -55 F -30 F (c) -14 F D) -12 F O F (F) 45 F G) 68 F The problem is unsolvable as it lacks additional information.
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Step 1Given data:Temperature of room is: T_(s)=30^(@)FStep 2According to Newton's law of cooling:{:[-(dT)/(dt)=k(T-T_(s))],[(dT)/(dt)+kT=T_(s)k],[e^(jt)(dT)/(dt)+kTe^(itt)=30 ke^(itt)],[(d(Te^(jt)))/(dt)=30 ke^(it)],[Te^(itt)=30e^(itt)+c],[T=Ce^(-kt)+30]:}Substitute values for temperatures after time 10 min i.e., T(10)=0.{:[0=ce^(-10 k)+3 ... See the full answer