Question

Newton's Law of Cooling states that the rate of change of the temperature of an object, T, is proportional to the difference of T and the temperature of the region, TR or dT over dt equals k times the quantity T minus T sub R end quantity. An object with core temperature of 1200°F is removed from a fire and placed in a region with a constant temperature of 80°F. After 1 hour, its core temperature is 830°F. What is the object's core temperature 4 hours after it is taken off the fire?

Answer 1

Answer:

- 278.4°F

Step-by-step explanation:

Temperature of Object ( T ) = 1200° F

Temperature of surrounding ( M ) = 80°F

Time ( t ) = 1 hour

dT / dt  ∝ ( M - T )

dT /dt ∝ | ( 80 - 1200 ) |

dT / dt = k ( 1120 )

(1200 - 830 ) / 1 = k ( 1120 )

hence k =  ( 1200 - 830 ) / 1120

              =   370 / 1120 = 0.33

what is the object's temperature (x )after 4 hours

( 1200 - x ) / 4  = 0.33 ( 1120 )

( 1200 - x ) / 4 = 369.6

hence x = 1200 -  ( 4 * 369.6 )

              = - 278.4 ° F