Frank’s automobile engine runs at 100∘c. one day, when the outside temperature is 15∘c, he turns off the ignition and notes that 5 minutes later, the engine has cooled to 70∘c. when will the engine cool to 40∘c? (use decimal notation. give your answer to the nearest whole number.)

the engine cool to 40 at 14.07 minutes

Explanation:

Given information

T(5) = 70

= 100

C = 15

Newton's law of cooling :

T(t) = C + ( - C)

where

T(t) = temperature at any given time

C = surrounding temperature

= initial temperature of heated object

k = cooling constant

to find the the time when the engine will be cooled down to 40, we first need to find the cooling constant, k

when t = 5, T(5) = 70

so,

T(t) = C + ( - C)

T(5) = 15 + (100 - 15)

70 = 15 + (85)

= (70 - 15) / 85

-5k = ln (55/85)

k = - ln (55/85) / 5

k = 0.087

thus, we have the eqaution

T(t) = 15 + (85)

now we can determine the time when T(t) = 40

40 = 15 + (85)

= (40-15)/85

-0.0087t = ln (25/85)

t = - ln (25/85)/0.087

t = 14.07 minutes

a high pressure system is a dense air mass that is usually cooler and drier than the surrounding air. a low pressure system is a less dense air mass that is usually wetter and warmer than the surrounding air.

in general, areas that experience high atmospheric pressure also experience fair weather. low pressure systems can cause the formation of clouds and storms. air usually flows from areas of high pressure to areas of low pressure..

more than, less

less than, more