Question

Suppose the rate of change of the temperature of a body is proportional to the difference...

Suppose the rate of change of the temperature of a body is proportional to the difference between & the temperature of the body and the temperature of the surrounding environment which is 35 . The k initial body temperature is 120 After 40 minutes, the temperature went to 60 .

a.) Find the differential equation with initial condition that models this situation.

b.) Solve to find the general solution using the technique of separation of variables. Call the constant C

c.) Use the initial condition to help find the constant C

d.) Use the fact that to find the value of the constant of proportionality k

e.) After how long will the temperature be 39 ?

Math   Calculus   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
The temperature T of a body will increase or decrease at a rate proportional to the...
The temperature T of a body will increase or decrease at a rate proportional to the temperature difference respectively below or above the surrounding temperature, T¯, the constant of proportionality being k. Derive an expression depicting the temperature of the body as a function of the time given that its initial temperature is T0. Sketch, by inspection, the graph of T = T(t) when T0 < T¯, and when T0 > T¯.
Newton’s Law of Cooling tells us that the time rate of chnge in temperature T(t) of...
Newton’s Law of Cooling tells us that the time rate of chnge in temperature T(t) of a body immersed in a medium of constant temperature A is proportional to the difference A − T.The DE modeling this is dT dt = k(A − T). A cup of hot chocolate is initially 170◦ F and is left in a room with an ambient temperature of 70◦ F. Suppose that at time t = 0 it is cooling at a rate of...
The rate of change of the temperature of an object is proportional to the difference between...
The rate of change of the temperature of an object is proportional to the difference between the temperature of the object and the temperature of the environment (Newton's Law). In addition, heat flows from the warm to the cold. Water is boiled in a saucepan and then removed from the heating element, so that the initial temperature of the water is 100 degrees Celsius, while the temperature of the room is 20 degrees Celsius and will be assumed to be...
Newton's Law of Cooling tells us that the rate of change of the temperature of an...
Newton's Law of Cooling tells us that the rate of change of the temperature of an object is proportional to the temperature difference between the object and its surroundings. This can be modeled by the differential equation dTdt=k(T−A)dTdt=k(T-A), where TT is the temperature of the object after tt units of time have passed, AA is the ambient temperature of the object's surroundings, and kk is a constant of proportionality. Suppose that a cup of coffee begins at 179179 degrees and,...
(1 point) Newton's Law of Cooling states that the rate of cooling of an object is...
(1 point) Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. Suppose t is time, T is the temperature of the object, and Ts is the surrounding temperature. The following differential equation describes Newton's Law dT/dt=k(T−Ts), where k is a constant. Suppose that we consider a 95∘C cup of coffee in a 25∘C room. Suppose it is known that the coffee cools at a...
15. Newton’s Law of Cooling. Newton’s law of cooling states that the rate of change in...
15. Newton’s Law of Cooling. Newton’s law of cooling states that the rate of change in the temperature T(t) of a body is proportional to the difference between the temperature of the medium M(t) and the temperature of the body. That is, dT/dt = K[M(t) - T(t)] , where K is a constant. Let K = 0.04 (min)-1 and the temperature of the medium be constant, M(t) = 293 kelvins. If the body is initially at 360 kelvins, use Euler’s...
A body at an unknown temperature is placed in a room which is held at a...
A body at an unknown temperature is placed in a room which is held at a constant temperature of 30° F. If after 10 minutes the temperature of the body is 0° F and after 20 minutes the temperature of the body is 15° F, find the unknown initial temperature.  I need to use MATLAB for this. Thankyou! Finals Answers:-30° F
The change in temperature in Kelvin and Celsius is the same, as it should be. QUESTION...
The change in temperature in Kelvin and Celsius is the same, as it should be. QUESTION Which represents the larger temperature change, a Celsius degree or a Fahrenheit degree? It's subjective and depends on the observer's judgment.One degree is the same on either scale.    It depends on the initial temperature.FahrenheitCelsius PRACTICE IT Use the worked example above to help you solve this problem. The temperature gradient between the skin and the air is regulated by cutaneous (skin) blood flow. If the...
1. Solve the given initial value problem. dy/dt = (t^3 + t)/(y^2); y(0) = 2 ....
1. Solve the given initial value problem. dy/dt = (t^3 + t)/(y^2); y(0) = 2 . 2. We know from Newton’s Law of Cooling that the rate at which a cold soda warms up is proportional to the difference between the ambient temperature of the room and the temperature of the drink. The differential equation corresponding to this situation is given by y' = k(M − y) where k is a positive constant. The solution to this equation is given...
QUESTION 4 When there is heat transfer from the lateral side of an infinitely long cylinder...
QUESTION 4 When there is heat transfer from the lateral side of an infinitely long cylinder of radius a into a surrounding medium, the temperature inside the cylinder depends upon the time t and the distance r from its longitudinal axis (i.e. the axis through the centre and parallel to the lateral side.) a. Write down the partial differential equation that models this problem. b. Suppose that the surrounding medium is at temperature zero and the initial temperature is constant...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT