# Specific Heat

• positive q = system has gained heat from the surroundings (endothermic)
• negative q = system has released heat to the surroundings (exothermic)
q depends on the change within the system, no on how the change occurs

• specific heat = measure the change in temperature that a known mass undergoes as it loses or gains a specific quantity of heat
Specific heat of water is 4.184 J/gşC

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 25.0şC to 48.0şC 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 = 25.0şC
Final Temperature = 48.0şC
Specific Heat (C) = ?

q = m . C . ∆T

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

849 J = (95.4 grams) (C) (23şC)

849 J = 2194.2 C

849 J/2194.2 = 2194.2/2194.2 C

C = 0.387 J/gşC

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 23şC and Cup B contains 50 grams of water at 89şC.

qlost = qgained

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

(50 grams) (4.184 J/gşC) (89şC - x) = (25 grams) (4.184 J/gşC) (x - 23şC)

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

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 = 67şC