Specific Heat

q depends on the change within the system, no on how the change occurs



Specific heat of water is 4.184 J/gC

Formulas to know:

                         q  =  m .  C  . ∆T 

                                 and


                          qlost  =  qgained

                             which means,

     mlost  .  Clost  .  ∆Tlost  =    mgained  .  Cgained  .  ∆Tgained  

∆T means a change in temperature represented by taking the final temperature minus the initial temperature.



Example: The temperature of a piece of copper with a mass of 95.4 grams increases from 25.0C to 48.0C when the metal absorbs 849 J of heat. What is the specific heat of copper?

Variables:
Mass = 95.4 grams
Heat = 849 J
Initial Temperature = 25.0C
Final Temperature = 48.0C
Specific Heat (C) = ?

q = m . C . ∆T

849 J = (95.4 grams) (C) (48.0C - 25.0C)

849 J = (95.4 grams) (C) (23C)

849 J = 2194.2 C

849 J/2194.2 = 2194.2/2194.2 C

C = 0.387 J/gC




Example:Calculate the final temperature if the following mixtures of water are placed together in the same cup: Cup A contains 25 grams of water at 23C and Cup B contains 50 grams of water at 89C.

qlost = qgained

mlost . Clost . ∆Tlost = mgained . Cgained . ∆Tgained

(50 grams) (4.184 J/gC) (89C - x) = (25 grams) (4.184 J/gC) (x - 23C)

(209.2) (89C - x) = (104.6) (x - 23C)

18618.8 - 209.2x = 104.6x - 2405.8

18618.8 + 2405.8 = 104.6x + 209.2x

21024.6 = 313.8x

21024.6/313.8 = 313.8/313.8 x

x = 67C