A liquid at temperature [tex]25^\circ F[/tex] is placed in an oven at temperature [tex]425^\circ F[/tex]. The temperature of the liquid increases at a rate 2 times the difference between the temperature of the liquid and that of the oven. Write a differential equation for the temperature [tex]T(t)[/tex] of the liquid.

Question

29-01-2024
Mathematics

High School

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A liquid at temperature [tex]25^\circ F[/tex] is placed in an oven at temperature [tex]425^\circ F[/tex]. The temperature of the liquid increases at a rate 2 times the difference between the temperature of the liquid and that of the oven. Write a differential equation for the temperature [tex]T(t)[/tex] of the liquid.

Answer :

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jaisharma131313 jaisharma131313 · Answer 1 · 2025-01-13T11:20:48-05:00

Final answer:

The differential equation for the temperature of a liquid being heated in an oven is expressed as dT/dt = 2(T_oven - T_liquid), capturing the dynamics of heat transfer.

Explanation:

The question asks us to write a differential equation for the temperature T(t) of a liquid, which is initially at 25°F and placed in an oven at 425°F. The rate of temperature increase of the liquid is twice the difference between the temperature of the liquid and that of the oven. This leads to the differential equation dT/dt = 2(T_oven - T_liquid), where T_oven is 425°F and T_liquid = T(t). In this situation, we are dealing with a first-order linear differential equation that models the thermal dynamics of a liquid being heated.