contestada

Suppose both cups are poured at the same time, and both are left sitting in the room that is 75°F. But this time,
milk is immediately poured into Cup 2, cooling it to an initial temperature of 162°F.
a. Use Newton’s law of cooling to write equations for the temperature of each cup of coffee after tt minutes has
elapsed.

Respuesta :

valenbraca

Answer:

The equations of both cups after t minutes is given by:

[tex]T_{Cup1}=75 °F+(180 °F-75 °F)e^{-0.2337min^{-1}*t}[/tex]

[tex]T_{Cup1}=75 °F+(162 °F-75 °F)e^{-0.2337min^{-1}*t}[/tex]

Step-by-step explanation:

The complete exercise says:

Two cups of coffee are poured from the same pot. The initial temperature of the coffee is 180°F, and is 0.2337 (for time in minutes).

Newton's law of cooling:

[tex]T=T_m+(T_0-T_m)e^{-kt}[/tex]

where,

[tex]T_m[/tex]= room temperature

[tex]T_0[/tex]= initial temperature

k=cooling constant

Hence,

Cup 1:

[tex]T_m[/tex]= 75 °F

[tex]T_0[/tex]= 180 °F

[tex]T_{Cup1}=75 °F+(180 °F-75 °F)e^{-0.2337min^{-1}*t}[/tex]

Cup 2:

[tex]T_m[/tex]= 75 °F

[tex]T_0[/tex]= 162 °F

[tex]T_{Cup1}=75 °F+(162 °F-75 °F)e^{-0.2337min^{-1}*t}[/tex]

Otras preguntas