At Westonci.ca, we make it easy for you to get the answers you need from a community of knowledgeable individuals. Ask your questions and receive detailed answers from professionals with extensive experience in various fields. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

A liquid at temperature 7575F is placed in an oven at temperature 450450. The temperature of the liquid increases at a rate 77 times the difference between the temperature of the liquid and that of the oven. Write a differential equation for the temperature T(t) of the liquid.

Sagot :

Answer: [tex]\dfrac{dT(t)}{dt}=77\times (450-T)[/tex]

Step-by-step explanation:

Given

The temperature of the liquid is [tex]75^{\circ}F[/tex] placed in an oven with temperature of [tex]450^{\circ}F[/tex].

Initially difference in temperature of the two

[tex]\Delta T=450-75\\\Rightarrow \Delta T=375^{\circ}F[/tex]

According to the question

[tex]\Rightarrow \dfrac{dT(t)}{dt}=77\cdot \Delta T\\\\\Rightarrow \dfrac{dT(t)}{dt}=77\times (450-T)\quad [\text{T=75}^{\circ}F\ \text{at t=0}][/tex]