Calculating Heat of Fusion Using Graph: A-F

[metalmagik]

I have a graph here separated into 5 different parts (A-B, B-C, C-D, D-E, E-F) It is a curve going upwards...I just need to know how to calculate the heat of fusion of the substance using the curve in the graph...I can use the formula and calculate the heat of fusion for each little piece but...do I add them after that? I'm just not really sure...any help is once again appreciated, if you need me to clarify or draw the graph I will, gladly. Thank you.

 

[Astronuc]

What is the curve?

The standard enthalpy change of fusion, also known as the heat of fusion, is the amount of thermal energy which must be absorbed or lost for 1 gram of a substance to change states from a solid to a liquid or vice versa. It is also called the latent heat of fusion or the enthalpy of fusion, and the temperature at which it occurs is called the melting point.

http://en.wikipedia.org/wiki/Heat_of_fusion

and perhaps better - http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/phase2.html#c1

 

[metalmagik]

It's a positive curve going upwards but its not really a curve it has constants in temperature every now and then but its going positive. I still don't understand how to interpret graphs from those links haha I am sorry please help me

 

[Astronuc]

During a phase change, temperature is essentially constant. The energy goes into transforming from solid to liquid.

What are the abscissa (x or horizontal scale) and ordinate (y or vertical scale) of the graph?

If the graphs show rise - constant - rise - constant - rise, then it may correspond to solid - melting - liquid - vaporizing - vapor (gas). The first constant temperature interval may coincide with the heat of fusion.

 

[metalmagik]

ah yes that's how it is exactly...thank you...how do i calculate the heat of fusion of the unknown substance by simply using that? There is also a chart which asks me for the change on kinetic energy and the change in potential energy how do i do that!

 

[metalmagik]

By the heat of fusion i mean for the ENTIRE graph (the whole substance and not just for the different segments

 

[Astronuc]

ah yes that's how it is exactly...thank you...how do i calculate the heat of fusion of the unknown substance by simply using that?

Answer this question - What are the abscissa (x or horizontal scale) and ordinate (y or vertical scale) of the graph? - and I will try to explain it. If the constant parts are horizontal, then the ordinate is temperature. If the constant parts are vertical then the abscissa is temperature.

There is also a chart which asks me for the change on kinetic energy and the change in potential energy how do i do that!

Kinetic or potential of what?

Increasing a temperature of a substance increases the kinetic energy of the molecules, more so for vapor than liquid, and more so for liquid than solid. Increasing temperature also increases the potential energy or potential to do work.

 

[metalmagik]

ordinate is temperature yes and abscissa is time in minutes. it is asking for the delta KE and delta PE for each line segment. How would I calculate this?

 

[Astronuc]

By the heat of fusion i mean for the ENTIRE graph (the whole substance and not just for the different segments

Heat of fusion applies only to the energy absorbed when a substance melts, i.e. changes from solid to liquid or liquid to solid.

Heat into a material would imply solid to liquid transformation. Heat out (removal) would imply 'freezing' or transformation from liquid to solid.

Unless, one has two different substances which melt at two different temperatures.

 

[metalmagik]

So does that mean that I can only calculate heat of fusion for those parts?

 

[Astronuc]

ordinate is temperature yes and abscissa is time in minutes. it is asking for the delta KE and delta PE for each line segment. How would I calculate this?

What other information is given.

If one is given a heat rate (or power, which = energy/time) then simply integrate the area of power * time to get energy, and the energy in the constant period would be heat of fusion for the solid to liquid transformation.

Is there a discussion in your text on the change in kinetic energy or potential energy as a function of temperature in a liquid or vapor?

Are you looking at the kinetic or potential energy from a molecular perspective?

See this - http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/kintem.html#c2

 

[metalmagik]

I do not know how I am looking at the KE or PE...i have only looked through packets and sheets to understand this topic becuse I Was given no instruction. but so heat rate = energy/time...and if I find heat of fusion for each segment is THAT the energy? if so then I will be able to do this

 

[Astronuc]

So does that mean that I can only calculate heat of fusion for those parts?

If there are two constant temperature parts, then I expect one is for melting (heat of fusion) and the other is for boiling or vaporization (heat of vaporization).

Yes, power (heat rate) = energy/time, so power * time = energy. Time is the time interval (e.g. t₂-t₁) over which heat is added (or subtracted if heat is removed).

A temperature increase would result in a change in potential energy or possibly kinetic energy, but I would need further information.

 

[metalmagik]

Oh ok thank you, yes, I understand the heat of fusion and vaporization now.

 

[metalmagik]

oh wait I am sorry it tells me the energy here, 200 J/minute

 

[metalmagik]

I can figure out the PE and KE thank you very much...there is another question concerning the Average KE of molecules in a larger solid compared to average KE of molecules in a smaller solid. It also says to compare their internal energies. Block A is 1 kg, Block B is 1 Gram, both temperatures are at 300 K

 

[Astronuc]

The molecular kinetic of a substance is dependent on temperature, not mass. The 'total' kinetic energy is off course related to the number of molecules and therefore to mass.

See - http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/kintem.html#c1

 

[Astronuc]

oh wait I am sorry it tells me the energy here, 200 J/minute

200 Joules/minute is the heat rate or power going into the substance. Make sure the time is compatible, i.e. in minutes.

The energy is just the area under the curve.

If the temperature is constant for 10 minutes, then at 200 J/min, 2000 J would be put into the substance.

Do you have a mass or number of moles into which the heat is input? Usually one works with energy/unit mass.

 

[metalmagik]

the mass is 10 kg, i don't have a number of moles...im still trying to find the KE of this substance, what exactly was the formula again? I remember you told me power = energy/time and i found all of that but how do I get the KE and PE?

 

[Astronuc]

the mass is 10 kg, i don't have a number of moles...im still trying to find the KE of this substance, what exactly was the formula again? I remember you told me power = energy/time and i found all of that but how do I get the KE and PE?

Just use the mass. Heat of fusion is often given by energy/unit mass.

See examples - http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/phase2.html#c1

How are potential and kinetic energy defined? Certainly increasing the temperature of a substance increases the molecular kinetic energy, as well as the potential energy.

 

[metalmagik]

How are potential and kinetic energy defined? Certainly increasing the temperature of a substance increases the molecular kinetic energy, as well as the potential energy.

oh okay I understand this a little better now...except that some of the chart is filled out and when the temp is not increasing...it still says that delta PE increases...why is this?

 

[Astronuc]

oh okay I understand this a little better now...except that some of the chart is filled out and when the temp is not increasing...it still says that delta PE increases...why is this?

Probably because it represent heat energy that can be released. When something freezes, it is because heat (energy) is being released, even though the temperature is constant. Similar, when something condenses, i.e vapor to liquid, heat is being released.

 

[metalmagik]

Oh alright, thank you very much for all your help