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THERMAL
EQUILIBRIUM
   Lesson #4
Objectives
 Define thermal
  equilibrium
Solve sample
  problems involving
  thermal equilibrium
Apply thermal
  equilibrium in daily
  life
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.


                 The thermometer
                 reads 98 °F
The thermometer was not removed
 until the time reached 5 minutes.


                  The thermometer
                  now reads 101 °F
      101 °F
Why did the    Easy! Because
temperature    they’re not      Bu..Bu..But..
change after   yet in thermal     I, I can’t
some time?     equilibrium!     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     Whatever.
   will beat you!!          Timmy.


      Holy!! My water is
     now getting warmer!
      Help me Timmy!!!
Don’t worry doggy, we’ll get
                               Really?
you some ice for you later
                               Thanks
                             But I
                          wonder how
                           many ice
                           will make
                           the juice
                          cold again?
Timmy needs help…

          But it seems that you lost your
                          magic powers..

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

         How are you going to help him?
First you need to        Ti = 15 °C
consider the condition   m = 200 g
of Doggy’s drink.

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
negative denotes   (where Q = mcΔT)
 heat released
Do you now have what it takes?

            Can you solve the problem of
                                Timmy?

Or do you wish to give up?


 Well then, let us see if you can use your
                 skills in problem solving.
Ti = 15 °C
              MIXED       Ti = 0 °C
m = 200 g
                          m=?




             Tf = 10 °C
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?

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Thermal equilibrium

  • 3. Solve sample problems involving thermal equilibrium
  • 4. Apply thermal equilibrium in daily life
  • 5.
  • 6. Quiet now children! So before we begin, eyes on the board please. Study the illustration.
  • 7. A thermometer is placed on the forehead of a kid with a fever. The thermometer reads 98 °F
  • 8. The thermometer was not removed until the time reached 5 minutes. The thermometer now reads 101 °F 101 °F
  • 9. Why did the Easy! Because temperature they’re not Bu..Bu..But.. change after yet in thermal I, I can’t some time? equilibrium! understand! Why?!
  • 10. 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.
  • 11. 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.
  • 12. 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.
  • 13. 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.
  • 14. You… you!!!!! Darn! You’ll pay for this!!! You’ll see! One day, I Whatever. will beat you!! Timmy. Holy!! My water is now getting warmer! Help me Timmy!!!
  • 15. Don’t worry doggy, we’ll get Really? you some ice for you later Thanks But I wonder how many ice will make the juice cold again?
  • 16.
  • 17. Timmy needs help… But it seems that you lost your magic powers.. ..and equipped only with the knowledge of thermal equilibrium. How are you going to help him?
  • 18. First you need to Ti = 15 °C consider the condition m = 200 g of Doggy’s drink. How much ice would be enough to cool down the temperature of the water? (mass) Tf = 10 °C
  • 19. 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.
  • 20. Or simply, it must follow the Law of Conservation of Energy ΔE = 0 No heat will flow out of the system
  • 21. Q+Q=0 Qlost + Qgained = 0 Qgained = - Qlost negative denotes (where Q = mcΔT) heat released
  • 22. Do you now have what it takes? Can you solve the problem of Timmy? Or do you wish to give up? Well then, let us see if you can use your skills in problem solving.
  • 23. Ti = 15 °C MIXED Ti = 0 °C m = 200 g m=? Tf = 10 °C
  • 24. Qgained = - Qlost mcΔT = - (mcΔT) mici(Tf-Tii) = - [mwcw(Tf-Tiw)] “i” subscript for ice “w” subscript for water
  • 25. 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?
  • 27. 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?