Question: A body initially at a temperature Ti cools by convection and radiation in a room where the temperature is T0. The body obeys Newton's law

A body initially at a temperature Ti cools by convection and radiation in a room where the temperature is T0. The body obeys Newton's law of cooling, which can be written dQ/dt = hA(T – T0 ),where A is the area of the body and h is a constant called the surface coefficient of heat transfer. Show that the temperature T at any time t is given by T = T0) + (Ti = T0)e–hat/mc where m is the mass of the body and c is its specific heat.

Step by Step Solution

★★★★★

3.48 Rating (164 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

dQ mcdT is heat loss as T diminishes by dT Th... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

10-P-T-T-P (147).docx

120 KBs Word File

Students Have Also Explored These Related Thermodynamics Questions!

A flutist assembles her flute in a room where the speed of sound is 342 m/s. When she plays the note A, it is in perfect tune with a 440 Hz tuning fork. After a few minutes, the air inside her flute...

The heat flow vector H = k?T, where T is the temperature and k is the thermal conductivity. Show that where then ? ? H = 0. T = 50 sin Ty cosh 2

William and Helen are a common law couple who contribute regularly to their RRSPs. William's annual contribution limit is $10,000, while Helen has a limit of $4,000. William will have a higher...

How were the calculations done? need help writing a lab report pls and thanks. Experiment H-1 Data Sheet Trial Al Pb Item - 2 Units Aluminium lead Type of metal sample Al Pb Mass of metal sample (ms)...

a. Example 13-1: Batch Reactor with an Exothermic Reaction Wolfram 1. Adiabatic Case: Use Wolfram to see whether you can find a trajectory that is ready to ignite and whose trajectory looks like a...

Explain how the principles of quantum mechanics are able address the issues. The development of quantum mechanical theory stems from several issues that could not be addressed by the principles of...

please could you help me with this. Newton's Law of Cooling Relates Temperature to Time In this course we start with the solution to Newton's mathematical equation that is solved using calculus. We...

Newton's law of cooling relates the rate at which a body cools to the difference in temperature between the body and the environment into which it is introduced. The formula is F(t)=T0+Cbt, where...

If C = 100, k = 0.1, and t is time in minutes, how long will it take a hot cup of coffee to cool to a temperature of 25C in a room at 20C? Newtons law of cooling says that the rate at which a body...

Calculate net income for tax purposes for each of the three taxpayers. Income tax reference: ITA 3. Taxpayer A Taxpayer B axpayer C Employment income Business income (loss) Property income (loss)...

Write a summary of a science topic of your choice.You must list at least two different types of sources (book, article, report, website, etc.) The quote may be a paraphrase or summary; The direct...

18. LO.7 What types of information are reported on the partnerships Schedule K? How does Schedule K relate to the partnerships Schedule M1 (or M3) and Schedule M2?

Select an adult at random. Define events T: person is over 6 feet tall, and B: person is a professional basketball player. Rank the following probabilities from smallest to largest. Justify your...

This ones got me stumped, you say to no one in particular. First day on the job; Id better get it right. Its the classification of notes payable in the statement of cash flows that has you in doubt....

Find a blog that concentrates on the taxation of partners and partnerships. Post a message defining the terms inside basis and outside basis and illustrating why the distinction between them is...

Consider a 2 3 design for fitting a first-order model. (a) Evaluate the D-criterion |(X'X) -1 | for this design. (b) Evaluate the A-criterion tr(X'X) -1 for this design. (c) Find the maximum scaled...

1. What fixed monthly payment is required to pay off a $5000 credit card balance in three years if the interest rate is 21.1% compounded monthly? 2. What is the amount of interest you will pay? 3. If...

Give an example of a gas dissolved in another gas. Is this mixture homogeneous?

How many 90-W, 120-V light bulbs can be connected to a 20-A, 120-V circuit without tripping the circuit breaker? (See the note in Exercise 26.18.)

(a) When the heating element is first turned on, what current does it draws and what electrical power does it dissipate? (b) When the heating element has reached an operating temperature of 280C...

A 400-, 2.4-W resistor is needed, but only several 400- , 1.2-W resistors are available (see Exercise 26.10). (a) What two different combinations of the available units give the required resistance...

Problem 1 4 - 1 4 Expected Return, Dividends, and Taxes [ LO 2 ] The Gecko Company and the Gordon Company are two firms whose business risk is the same but that have different dividend policies....

Help! Describe what happens to future value when a. The interest rate increases b. The number of compounding periods increases C. The amount of time over which something is invested decreases 2....

Thank you so much! (Preparing common-size financial statements) As the newest hire to the financial analysis group at Patterson Printing Company, you have been asked to perform a basis financial...