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# latent heat of vaporization formula

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.

Sensible heat

Sensible heat is the energy exchanged by a thermodynamic system that has as its sole effect a change of temperature.

The term is used in contrast to a latent heat, which is the amount of energy exchanged that is hidden, meaning it cannot be observed as a change of temperature. For example, during a phase change such as the melting of ice, the temperature of the system containing the ice and the liquid is constant until all ice has melted.

The sensible heat of a thermodynamic process may be calculated as the product of the body's mass (m) with its specific heat capacity (c) and the change in temperature (\Delta T):

Q_{sensible} = m c \Delta T \, .

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.

Sensible heat had a clear meaning in the writings of the early scientists who provided the foundation of thermodynamics. James Prescott Joule characterized it in 1847 as an energy that was indicated by the thermometer.

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.

Air source heat pumps

An air sourceheat pumpuses outside air as a heat source or heat sink. A compressor, condenser and refrigerant system is used to absorb heat at one place and release it at another.

## General

Outside air, necessarily existing at some temperature above absolute zero, is a heat container. An air-source heat pump moves ("pumps") some of this heat to provide hot water or household heating. This can be done in either direction, to cool or heat the interior of a building.

The main components of an air-source heat pump are:

• a heat exchanger, over which outside air is blown, to extract the heat from the air
• a compressor, which acts like a refrigerator but in reverse and raises the temperature from the outside air
• a way to transfer the heat into a hot water tank or heating system, such as radiators or under-floor heating tubes

## How air source heat pumps work

Heating and cooling is accomplished by moving a refrigerant through the heat pump's various indoor and outdoor coils and components. A compressor, condenser, expansion valve and evaporator are used to change states of the refrigerant from a liquid to hot gas and from a gas to a cold liquid. The refrigerant is used to heat or cool coils in a building or room and fans pull the room air over the coils. An external outdoor heat exchanger is used to heat or cool the refrigerant. This use of outside air has led to the term "Air Source" Heat Pump. The overall operation uses the concepts described in classic vapor compression refrigeration.

When the liquid refrigerant at a low temperature passes through the outdoor evaporator coils, the temperature of the outside air causes the liquid to boil. This change of state from liquid to a vapor requires a considerable amount of energy or "latent heat" which is provided by outside air passing over the coils.

This vapor is then drawn into the compressor where the temperature of the vapor is boosted to well over 100 degrees Celsius. At this point we have used heat from the outside air to change the liquid refrigerant to a gas and added an amount of compression "work" to raise the temperature of the vapor. The vapor now enters the condenser heat exchanger coils where it begins to transfer heat to the air being drawn across the coils. As the vapor cools, it condenses back to a liquid and in so doing releases and transfers considerable latent heat to the air passing over the condenser unit coils. We have used the heat energy of outside air to change the phase of the refrigerant and then released this heat for heating, a typical heat pump operation.

At this stage we now have a very cold liquid refrigerant compressed to a high pressure. The refrigerant is next passed through an expansion valve which turns it back to a low pressure cold liquid ready to re-enter the evaporator to begin a new cycle.

The heat pump can also operate in a cooling mode where the cold refrigerant is moved through the indoor coils to cool the room air.

## Efficiency

The 'Efficiency' of air source heat pumps is measured by the Coefficient of performance (COP). In simple terms, a COP of 3 means the heat pump produces 3 units of heat energy for every 1 unit of electricity it consumes. In mild weather, the COP of an air source heat pump can be up to 4. However, on a very cold winter day, it takes more work to move the same amount of heat indoors than on a mild day. The heat pump's performance is limited by the Carnot cycle and will approach 1.0 as the outdoor-to-indoor temperature difference increases at around âˆ’18 Â°C (0 Â°F) outdoor temperature for air source heat pumps. However, heat pump construction methods that enable use of carbon dioxide refrigerant extend the figure downward to -30 Â°C (-22 Â°F). A Geothermal heat pump will have less change in COP as the ground temperature from which they extract heat is more constant than outdoor air temperature.

Seasonally adjusted heating and cooling efficiencies are given by the heating seasonal performance factor (HSPF) and seasonal energy efficiency ratio (SEER) respectively.

The efficiency of a heat pump can be significantly affected by its original design. Many air source heat pumps began life as air conditioning units, designed for summer temperatures. In [http://www.globalenergysystems.co.uk/features_products/why_eco_air_boilers.html designing a heat pump] as a heat pump from inception great COPs and life cycles can be attained. The principal changes are in the scale and type of compressor and evaporator to allow [http://www.globalenergysystems.co.uk/how_it_works/coefficient_performance.html COP] of greater than 2 even down to -20Â°C.

• Typically draws approximately 1/3 to 1/4 of the electricity of a standard resistance heater for the same amount of heating, reducing utility bills. This typical efficiency compares to 70-95% for a fossil fuel-powered boiler.
• Few moving parts, reducing maintenance requirements. However, it should be ensured that the outdoor heat exchanger and fan is kept free from leaves and debris. Moreover, it must be borne in mind that a heat pump will have significantly more moving parts than an equivalent electric resistance heater or fuel burning heater.
• As an electric system, no flammable or potentially asphyxiating fuel is used at the point of heating, reducing the potential danger to users, and removing the need to obtain gas or fuel supplies (except for electricity).
• May be used to heat air, or water.
• The same system may be used for air conditioning in summer, as well as a heating system in winter.
• lower running costs, the compressor being the thing that uses most power - when i

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.

Answers:Gaseous water represents a small but environmentally significant constituent of the atmosphere. Approximately 99.99% of it is contained in the troposphere. The condensation of water vapor to the liquid or ice phase is responsible for clouds, rain, snow, and other precipitation, all of which count among the most significant elements of what we experience as weather. Less obviously, the latent heat of vaporization, which is released to the atmosphere whenever condensation occurs, is one of the most important terms in the atmospheric energy budget on both local and global scales. For example, latent heat release in atmospheric convection is directly responsible for powering destructive storms such as tropical cyclones and severe thunderstorms. Water vapor is also a potent greenhouse gas. Because the water vapor content of the atmosphere is expected to greatly increase in response to warmer temperatures, there is the potential for a water vapor feedback that could amplify the expected climate warming effect due to increased carbon dioxide alone. However, it is less clear how cloudiness would respond to a warming climate; depending on the nature of the response, clouds could either further amplify or partly mitigate the water vapor feedback. Fog and clouds form through condensation around cloud condensation nuclei. In the absence of nuclei, condensation will only occur at much lower temperatures. Under persistent condensation or deposition, cloud droplets or snowflakes form, which precipitate when they reach a critical mass.

Question:How much heat must be added to turn 3 grams of water into a vapor and what will be the final temperature after this much heat is added? The latent heat of vaporization (or the amount of heat required to turn the water into vapor) is 540 calories./grams.

Answers:At what temperature is the water before you heat it? If it is already at 100C, then it would take 540 x 3 = 1620 calories to do this and you would have steam at 100C. If this was 3 g water at room temperature, then more heat would be required to raise the temp of the water up to 100C.

Question:CoolingWater Vapor I usually don't have to do this, but I have spent the last 2 hours tying to figure this problem out and it seems impossibly complicated to me. PLEASE HELP IF YOU CAN! One mole of water vapor at 391 K cools to 280 K. The heat given off by the cooling water vapor is absorbed by 7 mol of an ideal gas, and this heat absorption causes the gas to expand at a constant temperature of 273 K. If the final volume of the ideal gas is 18 L, determine its initial volume. The specific heat of water is 4186 J/kg C and the latent heat of vaporization is 2.26 106 J/kg.

Answers:Fortunately for you, I had the same pain in the ass problem. Because I love using Yahoo Answers so much, I thought I'd contribute for once. Basically you just combine the equations for Heat and Isothermal Energy and then you can get that gosh darn answer. FYI, a more in depth solution below. Enjoy! First, Find Q: Q = Lv + mc(Tf-Ti) Q = Heat Lv = Latent Heat of Vaporization (2.26 * 10^6 J/kg) m = mass c = specific heat capacity (4186 J/kg*C) Tf = Final Temperature (391 K) Ti = Initial Temperature (280 K) m = 1 mol of water vapor = 18.02 g = 0.01802 kg. all other variables are given Q = (2.26 * 10^6 J/kg)(0.01802 kg) + (0.01802 kg) (4186 J/kg*C)(391 K - 280 K) Q = 49098.12 J Second, understand the isothermal process Q = W: Q = W because the internal energy is zero. The internal energy is zero because the temperature is constant (273 K). Third, use the isothermal equation, and find Vi: Q = W = nRTln(Vf/Vi) R = Gas Constant (8.31 J/K) T= Constant Termperature (273 K) Vf = Final Volume (18 L) Vi = Initial Volume All variables are given except for Vi (49098.12 J) = W = (7 mol)(8.31 J/K)(273 K)(ln(118 L/Vi)) dividing Q by nRT gives you: ln(18 L/Vi) = 3.091741 then, e^(ln(18 L/Vi)) = e^3.091741 e^ln cancels out so: 18 L/Vi = 21.903246 so, Vi = 18 L/21.903246 Vi = 0.821796 L P.S. In a sort of creepy way, I think you are in my class (CHENG), your picture looks familiar.