A roast turkey is taken out of the when its temperature has reached 185 F and is

Question

A roast turkey is taken out of the when its temperature has reached 185 F and is placed on a table in a room whose temperature is a constant 75 F. If the temperature of the turkey is 150 F after half an hour, find a function that represents the temperature of the turkey at time t. What is the temperature of the turkey after 45 minutes? When will the temperature have cooled to 100 F? A vat with 500 gallons of beer contains 4% alcohol by (volume). Beer with 6% alcohol is pumped into the vat at a rate of 5 /min and the mixture is pumped out at the same rate. Find a function that represents the amount alcohol in the mixture. Set up the differential equation and solve. Hint: To make the integration easier, factor out the negative coefficient of variable (the text uses ) before solving. What is the percentage (amt of alcohol/500) of alcohol after an hour? What is the percentage of alcohol at t rightarrow infinity.

Explanation / Answer

3.)Heat loss when temperature is T= k(T-75) dt = -c dT;

-(k/c)dt= dT/(T-75);

-(k/c)t=ln(T-75)+ constant;

T=75+ P*e^(-Q*t) ;where all the costant are combined in P& Q;

At t=0; T= 185---> P=110;

So,T=75+ 110*e^(-Q*t);

At t=30 min; T= 150--->

ln(75/110)=-Q*30;

Q=0.01277;

(a)T=75+ 110*e^(-0.01277*t)

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.