Specific Heat and Latent Heat

• Specific heat: = energy required to change a unit mass of a material by 1°C. Units: energy per unit mass per degree.
• Latent heat = energy required to change the state (gas, liquid, solid) of a unit mass of material. Units: energy per unit mass.

Both specific heat and latent heat are properties of a given material. In other words, every time the material is heated/cooled, no matter how quickly or by what heating process, the same amount of heat is transferred to reach the same state.

Change in energy of a substance:

To raise/lower its temperature:
DE = CpM DT

To change its state:
DE = LM

where
DE = change in energy
DT = temperature change
M = mass
Cp = specific heat
L = latent heat

• to increase the temperature
• to melt it
• to evaporate it
Energy is released when a substance
• cools
• condenses
• freezes

Energy units:

• Ergs (1 erg = 1 g cm2 s-2)
• Joules (1 J = 1 kg m2 s-2 = 107 ergs)
• Calories (1 cal = 4.184 J)

Total energy to raise temperature of 1.0 kg of water from 10°C to 110°C

Cpwater = 4.2 x 103 J kg-1 °C-1
Cpsteam = 2.0 x 103 J kg-1 °C-1
Lvaporization = 2.3 x 106 J kg-1
M = 1 kg

DE = energy to heat water to boiling point +
energy to change state +
energy to raise temperature of steam
= Cpwater MDT + LvaporizationM + CpsteamMDT
= (4.2 x 103 J kg-1 °C-1)(1 kg)(90°C) + (2.3 x 106 J kg-1)(1 kg) + (2.0 x 103 J kg-1 °C-1)(1 kg)(10°C)

= 2.7 x 106 J

Total energy released at midocean ridges by formation of new oceanic crust

Cpbasalt = 1.4 x 103 J kg-1 °C-1
Cpmagma = 1.0 x 103 J kg-1 °C-1
Lmelting = 4.0 x 105 J kg-1
Temperature of magma when erupted = 1300°C
Melting point 1200°C
Temperature of sea water = 0°C
Length of ridge = 60,000 km = 6 x 107 m
Crustal thickness = 5 km = 5 x 103 m
Average spreading rate 2 cm yr-1 = 2 x 10-2 m yr-1
Density of basalt 3 x 103 kg m-3

1. Mass of magma solidified (per year) = volume x density
= ridge length x crustal thickness * spreading rate* density
= (6 x 107 m)( 5 x 103 m)( 2 x 10-2 m yr-1)( 3 x 103 kg m-3)
=2 x 1013 kg yr-1

2. DE = energy to solidify and cool crust (per year)
= energy to cool magma to melting point +
energy to solidify magma +
energy to cool basalt to ocean water temperature

DE = Cpmagma MDT +
LmeltingM +
CpbasaltMDT
= (1.0 x 103 J kg-1 °C-1)(2 x 1013 kg)(100°C) +
(4.0 x 105 J kg-1)(2 x 1013 kg) +
(1.4 x 103 J kg-1 °C-1)(2 x 1013 kg)(1200°C)
= 2 x 1018 J + 8 x 1018 J + 3 x 1019 J

= (4 x 1019 J)(107ergs/ J)= 4 x 1026 ergs