THERMAL EQUILIBRIUM

Lesson #4

Objectives

Define thermal equilibrium

Solve sample problems involving thermal equilibrium

Apply thermal equilibrium in daily life

Toon Tales

What’s the title

of the lesson

again, Sheldon?

Mrs. Puff,

can we go

back to the

1st slide?

Quiet now children!So before we begin, eyes on the board please.Study the illustration.

A thermometer is placed on the forehead of a kid with a fever.

98 °F

After 30 seconds

The thermometer reads 98 °F

The thermometer was not removed until the time reached 5 minutes.

101 °F

After 5 minutes

The thermometer now reads 101 °F

Why did the temperature change after some time?

Easy! Because they’re not yet in thermal equilibrium!

Bu..Bu..But..I, I can’t

understand! Why?!

What!? Remember?

When two substances having different temperatures are introduced or kept together, heat flows from a substance at higher temperature to a substance at lower temperature.

To make it more correct, heat continues to be transferred until their

temperatures are equalized. When this stage is achieved, only we can say that we can say that the substances are

in thermal equilibrium.

Oohh.. So that explains why the liquid inside the thermometer rises as time

passes by.

Yes! That is why we need to wait for a few minutes before

taking the reading of the thermometer.

Of course. With that, the kid’s body and the thermometer will reach the same temperature

Hey! You keep on finishing my sentences! Why are you

late anyway?

So what? I already understand the lesson.

You… you!!!!! Darn!You’ll pay for this!!!You’ll see! One day, I

will beat you!! Whatever.

Timmy.

Holy!! My water is now getting warmer!

Help me Timmy!!!

Don’t worry doggy, we’ll get you some ice for you later Really?

Thanks

He he he… They

don’t know I have

fairy godparents!

But I wonder how

many ice will make the juice

cold again?

COSMO!!! WANDA!!!Where are you guys!?!?

But it seems that you lost your magic powers..

Timmy needs help…

..and equipped only with the knowledge of thermal equilibrium.

How are you going to help him?

First you need to consider the condition of Doggy’s drink.

Ti = 15 °Cm = 200 g

How much ice would be enough to cool down the temperature of the water? (mass)

Tf = 10 °C

The mixture of ice and water would eventually reach thermal equilibrium.

However, they must be in a closed system so that heat will completely transfer from one body to another.

Or simply, it must follow the Law of Conservation of Energy

ΔE = 0 No heat will flow out of the system

Q + Q = 0 Qlost + Qgained = 0

Qgained = - Qlost

(where Q = mcΔT)negative denotes heat released

Can you solve the problem of Timmy?

Do you now have what it takes?

Well then, let us see if you can use your skills in problem solving.

Or do you wish to give up?

Ti = 15 °Cm = 200 g Ti = 0 °C

m = ?

Tf = 10 °C

MIXED

Qgained = - Qlost

mcΔT = - (mcΔT) mici(Tf-Tii) = - [mwcw(Tf-Tiw)]

“i” subscript for ice “w” subscript for water

A 200 g sample of water at 353 K is mixed with 200 g of water at

283 K. What is the final temperature of the

mixture?

Test Yourself

3. A 100-g Aluminum block at 373 K is placed in 100 g of 281 K water. The final temperature of

the liquid is 298 K. What is the specific heat

of aluminum?