1. II. Heat 1 cal = 4.186 J Heat and energy A little bit of history:
Old theories
Robert von Mayer ( )
James Joule ( )
Hermann von Helmholtz ( )
1 cal = J
Calorie: the amount of heat required to raise the temperature of 1 gram of water from 14.5 ◦C to 15.5 ◦C.

2. 2. Specific heat
1 cal = J
2a. Heat capacity

3. 2. Calorimetry
ΔQ=cmΔT
Example: 200 g of water at the temperature of 80°C is placed into a 50 g glass at 20°C. What is the final temperature of the system.
mw = 200g
Tw = 80º C
cw=1.0cal/(gCº)
mg = 50g
Tg = 20º C
cg = 0.20cal/(gCº)
T=Tf - ?

4. Q = ±mL ΔQ = ±ΔmL ΔQ - ? 3. Phase transitions.
Latent heat: energy required for a material to change phase, even though its temperature is not changing.
Q = ±mL
ΔQ = ±ΔmL
Example: 100 g of ice at the temperature of -40°C should be melted and heated to the temperature of 20°C. Calculate needed heat.
m= 100g
Ti = -40º C
ci=0.5cal/(gCº)
T = 20º C
cw =1.0cal/(gCº)
Tc = 0º C
L = 80 cal/g
ΔQ - ?

5. Example: Ice and Water
200 g of ice at -40º C is mixed with 300 g of water at 20º C.
What will happen with ice and water?
mw = 300g
mi = 200g
Tw = 20º C
Ti = -40º C
ci=0.5cal/(gCº)
cw =1.0cal/(gCº)
Tc = 0º C
L = 80 cal/g
25 g of ice will be melted
The temperature of the mixture will be 0º C

6. Example
Energy is required for a material to change phase, even though its temperature is not changing.

7. Avogadro number and number of moles
One mole is the amount of substance that contains as many elementary entities as there are atoms in 12g of carbon -12
n - number of moles
N - number of molecules
NA - Avogadro number
msample - total mass of sample
m - mass of one molecule
μ=M - molar (atomic) mass (“weight”)
Molecular weight
Molar specific heat (molar heat capacity)

8. Question
A beaker contains kg of water. The heat capacity of the water is ___ J/˚C. Assume: the specific heat of water is 4000 J/(kg·˚C).
200
400
600
800

9. Question
The heat capacity of the water in a massless beaker is 800 J/˚C. The amount of heat needed to increase the temperature of the water from 15.0 ˚C to 30.0 ˚C is ___ kJ. 4 8 12 16

10. Question
A liter of water is put in a sauce pan on a stove. In order to heat the water at 10 ˚C/minute requires a heating power of ___ Watts. (Ignore the heat capacity of the pan. Assume the heat capacity of a liter of water is 4200 J/˚C.)
500
700
900
1100

11. Question
Block A: 1.0 kg, c = 400 J/(kg·˚C), initial temperature = 100 ˚C
Block B: 2.0 kg, c = 200 J/(kg·˚C), initial temperature = 0 ˚C
After the blocks are put into thermal contact and reach equilibrium, the final temperature is __ ˚C. 50 30 70 40

12. Example
How much heat does it take to heat 1.00 kg of water ice from 10 ˚C up to 100 ˚C and boil the water away as steam?

13. Example
A 10 g ice cube at 0 ˚C is put into 100 g of water at 20 ˚C. Does the ice cube melt completely? If not, the final temperature of the water + ice cube would be 0 ˚C. If so, what is the final temperature of the water?