## Niobium – Specific Heat, Latent Heat of Fusion, Latent Heat of Vaporization

**Specific heat of Niobium is ****0.26 J/g K**.

**Latent Heat of Fusion of Niobium is ****26.4 kJ/mol**.

**Latent Heat of Vaporization of Niobium is ****682 kJ/mol**.

**Specific Heat**

**Specific heat, or specific heat capacity, **is a property related to** internal energy** that is very important in thermodynamics. The **intensive properties c_{v}** and

**are defined for pure, simple compressible substances as partial derivatives of the**

*c*_{p}**internal energy**and

*u(T, v)***enthalpy**, respectively:

*h(T, p)*where the subscripts **v** and **p** denote the variables held fixed during differentiation. The properties **c _{v} **and

**c**are referred to as

_{p}**specific heats**(or

**heat capacities**) because under certain special conditions, they relate the temperature change of a system to the amount of energy added by heat transfer. Their SI units are

**J/kg.K**or

**J/mol K**.

**Different substances **are affected to **different magnitudes **by the **addition of heat**. When a given amount of heat is added to different substances, their temperatures increase by different amounts.

**Heat capacity** is an extensive property of matter, meaning it is proportional to the size of the system. **Heat capacity C** has the unit of energy per degree or energy per kelvin. When expressing the same phenomenon as an intensive property, the **heat capacity** is divided by the amount of substance, mass, or volume. Thus the quantity is independent of the size or extent of the sample.

**Latent Heat of Vaporization**

In general, when a material **changes phase** from solid to liquid or from liquid to gas, a certain amount of energy is involved in this change of phase. In the case of liquid to gas phase change, this amount of energy is known as the **enthalpy of vaporization** (symbol ∆H_{vap}; unit: J), also known as the **(latent) heat of vaporization** or heat of evaporation. As an example, see the figure, which describes the phase transitions of water.

Latent heat is the amount of heat added to or removed from a substance to produce a phase change. This energy breaks down the attractive intermolecular forces and must provide the energy necessary to expand the gas (the **pΔV work**). When latent heat is added, no temperature change occurs. The enthalpy of vaporization is a function of the pressure at which that transformation takes place.

**Latent Heat of Fusion**

In the case of solid to liquid phase change, the change in enthalpy required to change its state is known as the enthalpy of fusion (symbol ∆H_{fus}; unit: J), also known as the **(latent) heat of fusion**. Latent heat is the amount of heat added to or removed from a substance to produce a phase change. This energy breaks down the attractive intermolecular forces and must provide the energy necessary to expand the system (the **pΔV work**).

The liquid phase has higher internal energy than the solid phase. This means energy must be supplied to a solid to melt it. Energy is released from a liquid when it freezes because the molecules in the liquid experience weaker intermolecular forces and have higher potential energy (a kind of bond-dissociation energy for intermolecular forces).

The temperature at which the phase transition occurs is the **melting point**.

When latent heat is added, no temperature change occurs. The enthalpy of fusion is a function of the pressure at which that transformation takes place. By convention, the pressure is assumed to be 1 atm (101.325 kPa) unless otherwise specified.

## Niobium – Properties

Element | Niobium |
---|---|

Atomic Number | 41 |

Symbol | Nb |

Element Category | Transition Metal |

Phase at STP | Solid |

Atomic Mass [amu] | 92.90638 |

Density at STP [g/cm3] | 8.57 |

Electron Configuration | [Kr] 4d4 5s1 |

Possible Oxidation States | +3,5 |

Electron Affinity [kJ/mol] | 86.1 |

Electronegativity [Pauling scale] | 1.6 |

1st Ionization Energy [eV] | 6.7589 |

Year of Discovery | 1801 |

Discoverer | Hatchet, Charles |

Thermal properties | |

Melting Point [Celsius scale] | 2477 |

Boiling Point [Celsius scale] | 4744 |

Thermal Conductivity [W/m K] | 53.7 |

Specific Heat [J/g K] | 0.26 |

Heat of Fusion [kJ/mol] | 26.4 |

Heat of Vaporization [kJ/mol] | 682 |

## Niobium in Periodic Table

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