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# latent heat of fusion equation

From Wikipedia

Latent heat

Latent heat is the heat released or absorbed by a chemical substance or a thermodynamic system during a change of state that occurs without a change in temperature, meaning a phase transition such as the melting of ice or the boiling of water. The term was introduced around 1750 by Joseph Black as derived from the Latin latere, to lie hidden.

In meteorology, latent heat flux is the flux of heat from the Earth's surface to the atmosphere that is associated with evaporation or transpiration of water at the surface and subsequent condensation of water vapor in the troposphere. It is an important component of Earth's surface energy budget. Latent heat flux is commonly measured with the Bowen ratio technique, or by eddy covariance.

## Usage

Two of the more common forms of latent heat (or enthalpies or energies) encountered are latent heat of fusion (melting) and latent heat of vaporization (boiling). These names describe the direction of energy flow when changing from one phase to the next: from solid to liquid, and to gas.

In both cases, the change is endothermic, meaning that the system absorbs energy on going from solid to liquid to gas. The change is exothermic (the process releases energy) for the opposite direction. For example, in the atmosphere, when a molecule of water evaporates from the surface of any body of water, energy is transported by the water molecule into a lower temperature air parcel that contains less water vapor than its surroundings. Because energy is needed to overcome the molecular forces of attraction between water particles, the process of transition from a parcel of water to a parcel of vapor requires the input of energy causing a drop in temperature in its surroundings. If the water vapor condenses back to a liquid or solid phase onto a surface, the latent energy absorbed during evaporation is released as sensible heat onto the surface. The large value of the enthalpy of condensation of water vapor is the reason that steam is a far more effective heating medium than boiling water, and is more hazardous.

The terms sensible heat and latent heat are not special forms of energy, instead they characterize the same form of energy, heat, in terms of their effect on a material or a thermodynamic system. Heat is thermal energy in the process of transfer between a system and its surroundings or between two systems with a different temperature.

Both sensible and latent heats are observed in many processes while transporting energy in nature. Latent heat is associated with the phase changes of atmospheric water vapor, mostly vaporization and condensation, whereas sensible heat is energy transferred that affects the temperature of the atmosphere.

## History

The term latent heat was introduced around 1750 by Joseph Black, and is derived from the Latin latere, meaning to lie hidden. In 1847, James Prescott Joule characterized latent energy as the energy of interaction in a given configuration of particles, i.e. a form of potential energy, and the sensible heat as an energy that was indicated by the thermometer, relating the latter to thermal energy.

## Specific latent heat

A specific latent heat (L) expresses the amount of energy in form of heat (Q) required to completely effect a phase change of a unit of mass (m), usually , of a substance as an intensive property:

L = \frac {Q}{m}

Intensive properties are material characteristics and are not dependent on the size or extend of the sample. Commonly quoted and tabulated in the literature are the specific latent heat of fusion and the specific latent heat of vaporization for many substances.

From this definition, the latent heat for a given mass of a substance is calculated by

Q = {m} {L}

where:

Q is the amount of energy released or absorbed during the change of phase of the substance (in kJ or in BTU),
m is the mass of the substance (in kg or in lb), and
L is the specific latent heat for a particular substance (kJ-kgmâˆ’1 or in BTU-lbmâˆ’1), either Lf for fusion, or Lv for vaporization.

## Table of latent heats

The following table shows the latent heats and change of phase temperatures of some common fluids and gases.

## Latent heat for water

The latent heat of condensation of water in the temperature range from âˆ’40 Â°C to 40 Â°C is approximated by the following empirical cubic function:

L_{water}(T)=-0.0000614342 T^3+0.00158927 T^2-2.36418 T+2500.79

with a determination coefficient of R^2=0.999988, where T is in Â°C.

Question:1. A cube of ice is taken from the freezer at -8.1 C and placed in a 91-g aluminum calorimeter filled with 2.8E2 g of water at room temperature of 22.0 C. The final situation is observed to be all water at 17.5 C. What was the mass of the ice cube? hint: The heat lost by the aluminum and 2.8E2 g of liquid water must be equal to the heat gained by the ice in warming in the solid state, melting, and warming in the liquid state. 2.An iron boiler of mass 2.1E2 kg contains 8.0E2 kg of water at 22 C. A heater supplies energy at the rate of 5.2E4 kJ/h. a) How long does it take for the water to reach the boiling point? b) How long does it take for the water to all have changed to steam? 3. What mass of steam at a temperature of 100.0 C, must be added to 4.1 kg of ice at a temperature of 0.0 C to yield liquid water having a temperature of 15.0 C?

Answers:Your questions here arenot impossible, but very simple. You just need to use the following equation: Q = mc(ice) T + mL(fusion) + mc(water) T + mL(vapor) + mc(vapor) T + Mc(container) T where Q is the change in heat energy, m is the mass of water, M is the mass of the container, L is the latent heat (this can be latent heat of fusion or latent heat of vaporization depending on the phase transition), c is the specific heat capacity, and T is the change in temperature. So here you must calculate the net Q by adding contributions from (1) changing temperature of ice, (2) transition from ice to water, (3) changing temperature of water, and (4) changing temperature of container. Note that some terms in the equation is not relevant. It depends on the question.

Question:

Answers:Energy to melt = Latent heat * mass = 11 J/g * 15 g = 165 J