_{C}=T

_{A}and system C must be in thermal equilibrium with system B also. This illustrates the zeroth law of thermodynamics stating that

if two systems are in thermal equilibrium with each other and a third system is in thermal equilibrium with one of them, then it is in thermal equilibrium with the other also.

## 2.1 Work

_{ext}is the external pressure of the surroundings, and the minus sign is needed to satisfy the convention that work done by the system should be negative (Fig. 2.1).

## 2.2 Heat

^{−1}K

^{−1}, while the specific heat capacity, \(C_{s}\), is the amount of heat for 1 K temperature increase per gram of material with the unit J g

^{−1}K

^{−1}. Using the molar or specific heat capacities Equation (2.3) would then respectively become:

^{−1}K

^{−1}) from 25 to 50 °C. Using Eq. (2.5), we then arrive at 1882 J.

## 2.3 The First Law

_{P}is thus higher than the constant volume heat capacity C

_{V}. Mathematically, C

_{V}relates \(\Delta T\) to the change in internal energy:

_{P}links \(\Delta T\) to the enthalpy change

## 2.4 Thermochemistry: Enthalpy Changes in Chemical Reactions

_{f}is added to indicate that is the enthalpy of formation and the superscript

^{o}that it relates to pure substances at SATP. For example, the gas N

_{2}and the solid graphite are the most stable form of elements N and C at standard conditions and their enthalpies of formation (\(\Delta H_{f}^{o} )\) have been set to zero. Thermochemists have constructed consistent databases with standard enthalpies of formation that can be used to calculate the enthalpy of reaction at standard conditions and making use of reaction stoichiometry.

_{12}H

_{22}O

_{11}; s) to CO

_{2}(aq) and water (l) at 1 bar. The relevant reaction and enthalpy of formations are:

Reaction | \(C_{12} H_{22} O_{11} \left( s \right)\) + | \(12 O_{2} \left( g \right)\) | \(\to\) | \(12 CO_{2} \left( {aq} \right) +\) | \(11 H_{2} O\left( l \right)\) |
---|---|---|---|---|---|

\(\Delta H_{f}^{o}\) | −2226.1 kJ mole ^{−1} | 0 kJ mole ^{−1} | −412.9 kJ mole ^{−1} | −258.8 kJ mole ^{−1} |

^{−1}(i.e. specific combustion enthalpy) rather than kJ mol

^{−1}, the unit used for enthalpy of formation \(\left( {\Delta H_{f}^{o} } \right)\). This specific combustion enthalpy is a measure of the energy density.

^{−1}and differ substantially, their respective specific combustion enthalpies are more alike: −55.5, −51.9, −50.4, −49.5 and −48.6 kJ g

^{−1}, respectively. For comparison, typical specific combustion enthalpies in kJ g

^{−1}of kerosene (−46.2), diesel (−44.2), crude oil (−43) are also in this range, while those of anthracite coal (−32.5), lignite coal (−15), wood (−15 to −20) and peat (−15 to −20) are much lower.

## 2.5 Enthalpy Changes During Phase Changes

## 2.6 Turning Ice into Steam: Latent and Sensible Heat

_{s}) of 2.09 J g

^{−1}K

^{−1}. For one gram of ice, 41.8 J (20 \(\times\) 2.09) will be required to reach the melting point of ice. At the melting point, 0 °C, further addition of heat will melt the ice but the system remains at the same temperature, and 331 J will be needed to convert one gram of ice into liquid (enthalpy of fusion). Further addition of heat will warm up the water and 418 J are required to reach the boiling point at 100 °C (since water has a specific heat capacity of 4.18 J g

^{−1}K

^{−1}). At the boiling point, liquid water will gradually turn into steam (evaporate), and this requires 2260 J (enthalpy of vaporization), but temperature does not change. Finally, further addition of heat will increase the temperature of the steam. To reach 120 °C, this will require an additional 36.8 J, because steam has a specific heat content of 1.84 J g

^{−1}K

^{−1}. The total energy required is about 3088 J, of which 84 % is used for phase changes (10.7 % for melting and 73.2 % for boiling) and does not result in a temperature increase. The energy consumed or released during phase transitions at a constant temperature is also known as ‘hidden’ or latent heat. This contrast with sensible heat, that results in a temperature change of the system. Latent heat fluxes are an important component of Earth’s surface energy budget, e.g., the evaporation/transpiration at the Earth surface and subsequent condensation of water in the troposphere. In the Earth’s interior, latent heat is also released if the liquid outer core crystallizes at the inner core boundary.

## 2.7 Adiabatic Changes, Lapse Rate, Geothermal Gradient and Potential Temperature

^{−2}) and \(z\) as height (m) to eliminate the pressure term, we eventually arrive at the lapse rate:

^{−1}K

^{−1}. This theoretical estimate for the dry air is fully consistent with the experience-based lapse rate of 1 °C per 100 m (Fig. 2.5).

_{0}is the reference pressure, T is the current temperature in K, R is the gas constant and \(C_{P}\) is the specific heat capacity at constant pressure. Meteorologists use a value 0.286 for the ratio \(\frac{R}{{C_{P} }}\). Potential temperature (\(\theta\)) in the ocean is always lower than the actual temperature by about 0.1 K for every km depth increase. This limited increase of in situ water temperature relative to potential temperature is due to the large heat capacity of water.

Property | Unit | Core-mantle boundary | Inner core boundary |
---|---|---|---|

Gravity, g | m s ^{−2} | 10.7 | 4.4 |

Density, \(\rho\) | kg m ^{−3} | 9900 | 12,980 |

\(C_{P}\) | J K ^{−1} kg^{−1} | 815 | 728 |

T | K | 3700 | 5000 |

Volume expansion coefficient, \(\alpha_{P}\) | 10 ^{−6} J kg^{−1} | 18.0 | 9.7 |