Molar Heat Capacities of Gases, Equipartition of Energy & Degrees of Freedom

This physics video tutorial explains how to calculate the molar heat capacity of a monoatomic gas and a diatomic gas. it gives a simple formula to achieve this. In addition, it discusses the equipartition of energy principle as it relates to the average translational kinetic energy for each degree of freedom for a molecule. This video contains plenty of examples and practice problems.
Boyle's Law Practice Problems:
• Boyle's Law Practice P...
How Does a Bike Pump Work?
• How Does a Bike Pump W...
Charles Law:
• Charles' Law
Gay Lussac's Law:
• Gay Lussac's Law Pract...
Avogadro's Law:
• Avogadro's law Practic...
Ideal Gas Law Problems:
• Ideal Gas Law Physics ...
_____________________________
Translational Kinetic Energy:
• How To Calculate The A...
Molecular Speed of Gases:
• Molecular Speed of Gas...
Mean Free Path and Free Time:
• Mean Free Path, Mean F...
RMS vs Average Speed:
• Root Mean Square Speed...
Phase Diagrams of H2O & CO2:
• Phase Diagrams of Wate...
____________________________
Relative Humidity & Dew Point:
• Relative Humidity - De...
Fick's Law of Diffusion:
• Fick's Law of Diffusio...
Open Vs Closed Vs Isolated System:
• Open System, Closed Sy...
First Law of Thermodynamics:
• First Law of Thermodyn...
Final Exams and Video Playlists:
www.video-tuto...
Physics PDF Worksheets:
www.video-tuto...

[@TheOrganicChemistryTutor]

Final Exams and Video Playlists: www.video-tutor.net/ Full-Length Math & Science Videos: www.patreon.com/mathsciencetutor/collections

[@ICantSeeYourRepliesDickhead]

u r awesome

[@aprotutor]

A diatomic molecule has 3 translational degrees of freedom. A diatomic molecule has only 1 vibrational degree of freedom. A diatomic molecule has 2 rotational degrees of freedom. So, a diatomic molecule has a total of 5 degrees of freedom at moderately low temperatures, when vibrational motion is not excited yet. A diatomic molecule has a total of 6 degrees of freedom at high temperatures.

[@nasserBack]

Useful for physical chemistry also not just physics

[@user-pb4jg2dh4w]

You need to increase this interval of audible frequencies in your videos to make them more clear [200-600] Hz

[@gbolagadeolajide6091]

In the last example, it seems to me that you calculated not translational KE (as the question required) but total KE - which includes (1) translational KE, and (2) rotational KE.

[@PriyanshuBhanja]

Correct thats what i was thinking in triatomic we have 3 translational and 3 rotatory here we will have an addition vibratory so its gonna be 3/7*3/2kt if i am not wrong

[@diojoestar4766]

I have a question regarding question 3. the molecule has 7 degrees of freedom. But from what I know there are only 3,linear freedoms, aka translation along Cartesian axes. Hence the other 4 are probably the rotational motions in x,y and z axes and some other things beyond HS. As the question is asking about transnational KE shouldn't we take 3/2 *kt instead of 7/2*kt?

[@GracieJohnston]

That's what I thought too

[@raanoooshh9296]

I thought so too

[@suyashsngh250]

3(Translational) + 2(Rotational) + 2(Vibrational) = 7 Diatomic gases at high temp have 7 degree of freedom in real life, so it's not imaginary.

[@nellvincervantes6233]

But vibrational energy is a potential energy and not kinetic energy. If he said total energy, then no confusion. 🤔

[@tunacannot]

@@nellvincervantes6233 vibrational contains one potential and one kinetic, so I guess there is one extra degree of freedom to think about.

[@bemnettesfaye757]

How do we know the degree of freedom of each element ? Is there any way to know , if there is tell me .

[@Bereket2D]

mono atomic gases have three degree di atomic gases have five degree tri atomics have seven degree

[@thedrunkenfish5855]

@@Bereket2Dwhat about something like propene(C3H6) ?

[@youngsnoopy9342]

Thank you man

[@JohanManojMathew]

Thanks and God bless.

[@vardaan1184]

you're the best. thankyou.

[@johnhopkins358]

who the hell put physics in my chemistry

[@Displ4c]

Ong

[@TheBetterBoma]

Who put chemistry in physics?

[@wangchakip8551]

did you consider vibration?

[@ayaabdel-meged3770]

شكراً

[@aka3673]

Do u have a separate lecture on that

[@vjosaveselaj3788]

Thank you so much

[@MrBlattgeist]

If you compare the molar heat capacity of Cl2, I2 and H2, at ambient temperature, apparently I2 has the highest, but since they are all 3 diatomic molecules with a degree of freedom of 5(at ambient temperature) I don't understand why their molar heat capacity is different. Can someone explain to me why?

[@peybak]

It might be because I2 is a bigger molecule. It takes up more heat to vibrate it and so on.

[@yadpreetcheema4806]

isn't this specific heat instead of heat capacity

[@diojoestar4766]

the full name is specific heat capacity. specific heat capacity and molar heat capacities are quite different. specific heat capacity expresses heat required to raise temp per unit temperature (1 Kelvin) and per unit "mass" (1 KG). molar heat capacity expresses heat required to raise temp per unit temperature (1 Kelvin) and per unit "moles" (1 mol). I assume I dont need to explain what mole is. while its easier to use KG and by extension Specific heat capacity, it is important to realize KG is a unit we devised for trade, macro atomic phenomenon deals with chunks of molecules in integral multiples moles(number of molecular weight) and NUMBER OF equivalent weights not KG so molar heat capacity is necessary to explain them.

[@anushkamandekar8494]

Isn't Q=nCpdT ? then for monoatomic gas Cp =3/2 R...pls correct me if I am wrong

[@davidog8298]

Cp = 5/2 R

[@tvykz]

Cp will always be one R greater than Cv, so if Cv = 3/2R as for a monotonic, Cp = 3/2R + R = 5/2R

[@nellvincervantes6233]

His question is why the uploader used Cv instead of Cp. Thats also my confusion too.

[@nellvincervantes6233]

Hmmm maybe because, from equations: dU = Tds - PdV dH = Tds + VdP Since theres no applied work, PdV = 0. Hence, dU = Tds We know that dU = Cv*dT and dS = Q/T (for closed system assuming no entropy generated) Cv*dT = Q And also for ideal gas (mono atomic gas), dU = (3/2)kdT Also, dH = Cp*dT Note that Cp = Cv + R/m (where m = molar mass of molecule) (Im not sure about this one) We can conclude also that VdP = (R/m)dT.

[@yanbingzhu4650]

Is translational kinetic energy the same to kinetic energy?

[@seiya221b]

translational means when a body moves more distance than its size and rotational is when it moves about in its axis. Kinetic energy can be translational and rotational.(correct me if I'm wrong😅)

[@guidancecorner8753]

nice video, you can find a comprehensive note on www.guidancecorner.com/heat-capacities-of-gases/ about heat capacities of gases and their units along with heat capacity formula. this whole article covers the following elements. #HeatCapacityOfGases #SpecificHeatCapacityUnits #heatcapacityofwater #heatcapacityofair #specificheatofhydrogen #specificheatcapacityofmethane again, nice video transcription and very good style to elaborate on things. thanks! regards Sumaira Alvi

[@katelynwilliams6930]

how does N2 have 5 degrees of freedom? i thought the number of degrees of freedom was 3 times the number the atoms, which for N2 would be 2 atoms, so the DOF would be 6???

[@stephenhawks3941]

katelyn williams no youre wrong, for diatomic gases , it is 5 and triatomic bent its 6

[@iPadStroller]

@@stephenhawks3941 it is 7, but in general, the two vibrational modes of a diatomic gas molecule are frozen out at room temperature

[@diojoestar4766]

3 are linear, i.e. along x,y, and z axes. the other 2 are rotational motions, 1 where the axis of rotation is along the bond and 1 where the axis of rotation is perpendicular to bond.

[@nabanitagoswami6652]

kzbin.info/www/bejne/oJzIgnSFbd10pMk

[@matthewvalencia8638]

@@nabanitagoswami6652 thank you

[@janmjayverma9982]

Thanks sa,

[@user-pb4jg2dh4w]

Thank you 😊