Great to have you back, sir. I had previously worked with the same problem, which after solving yielded the same result. And then tried to solve it in a non-classical, relativistic way .my initial goal was to find the potential energy of the entire system using relativistic way calculating energy (Swartzchild interior solution) , which was complicated. Based on your expertise in this field, I believe working on relativistic physics in your upcoming videos will be very brilliant and intresting like this one.
Hydrogen exists in monatomic form in a star because the temperature is so high. If it were diatomic, we'd have to use (5/2)kT instead of (3/2)kT as diatomic molecules have rotational kinetic energy as well as translational.
can you do about geothermal model of the earth probably? using heat equation on steady state with a core that generates heat and a mantle. is it reasonable?
Hey Dr. Ben, it's great to see you back! I really enjoyed your recent video on the temperature of a star, especially after such a lon break. Your content always brings out some of the most interesting problems in physics! I was thinking, as a follow-up to this thermodynamics topic, what if you did a video exploring how temperature changes over time for an object in a completely empty vacuum? Specifically, if we consider an object with a certain initial temperature in an ideal vacuum (with no surrounding objects), how does its temperature evolve over time as it radiates heat away? I've been trying to come up with a satisfying equation for this, but it seems like Newton's law of cooling might not fully apply in this scenario. I feel like this could be a really fascinating continuation of your recent video. Also, I wanted to say that I'm deeply sorry for your loss, and I admire your resilience in continuing to share such amazing content. Looking forward to more thought-provoking problems from you!
Just for fun (as almost all assumptions are incorrect), assume: - constant density r - constant specific heat capacity c - uniform temperature T(t) - black body radiation Then, thermal energy is (up to a constant) r•c•V•T(t) (where V is the volume) and radiated power is s•A•T(t)⁴ (where s is Stephan-Bolzmann constant and A is the area of the object). Equating the loss of thermal energy with the radiated power: r•c•V•(dT/dt) = -s•A•T⁴ This is a simple differential equation which provides T(t) :^) If I didn't mess up, the result is T(t) = T(0)/[(1 + bt)^(1/3)] where b = 3•s•A•T(0)³/(r•c•V).
Thanks for your kind words, I'm always happy to see your comments! I've just recorded another video today and hope to get it uploaded soon. Cooling of a black body is on my to-do list, this could of course become arbitrarily complicated but I was thinking of doing it using a simple model like the one proposed by the commenter above.
Sir after doing some analysis using the Stefan-Boltzmann law I found out that this model suggests that the intensity released by a star is proportional to the mass of the star raised to the power of 4 ! I find that quite interesting
![BLACK BAG - Official Trailer [HD] - Only in Theaters March 14](http://i.ytimg.com/vi/Du0Xp8WX_7I/mqdefault.jpg)
Prof takes a break and then the first video he posts is calculating temperature of the star 💀
I had to think of something impressive for my return!
Great to have you back, sir. I had previously worked with the same problem, which after solving yielded the same result. And then tried to solve it in a non-classical, relativistic way .my initial goal was to find the potential energy of the entire system using relativistic way calculating energy (Swartzchild interior solution) , which was complicated. Based on your expertise in this field, I believe working on relativistic physics in your upcoming videos will be very brilliant and intresting like this one.
Thanks for your support. Solving this one relativistically certainly sounds complicated!
7:32 3/2kT term is definded as KE per gas molecule , here hydrogen is diatomic so M/2mH h2 molecules ( where mH= mass of hydro. atom)
This makes 3/4kT( M/mH)
T= 4GMmH/5kR
Hydrogen exists in monatomic form in a star because the temperature is so high. If it were diatomic, we'd have to use (5/2)kT instead of (3/2)kT as diatomic molecules have rotational kinetic energy as well as translational.
Yes, I did a mistake but why multiplied by 2 still can't get that
The hydrogen atoms are ionised due to the high temperature, so each hydrogen atom contributes two separate particles, a proton and an electron.
Welcome back, many thanks!
Thanks, good to hear from you!
can you do about geothermal model of the earth probably? using heat equation on steady state with a core that generates heat and a mantle. is it reasonable?
I suppose the complication is that you probably need to account for convection in the mantle!
@@DrBenYelverton i see!
brilliant! your work in this channel is priceless, thank you
Thanks for your kind words! Glad you are enjoying the videos.
Great video that shows the power of estimation theory!
Thanks!
Thank you - it's amazing how well simple models work sometimes!
Hey Dr. Ben, it's great to see you back! I really enjoyed your recent video on the temperature of a star, especially after such a lon break. Your content always brings out some of the most interesting problems in physics!
I was thinking, as a follow-up to this thermodynamics topic, what if you did a video exploring how temperature changes over time for an object in a completely empty vacuum? Specifically, if we consider an object with a certain initial temperature in an ideal vacuum (with no surrounding objects), how does its temperature evolve over time as it radiates heat away? I've been trying to come up with a satisfying equation for this, but it seems like Newton's law of cooling might not fully apply in this scenario. I feel like this could be a really fascinating continuation of your recent video.
Also, I wanted to say that I'm deeply sorry for your loss, and I admire your resilience in continuing to share such amazing content. Looking forward to more thought-provoking problems from you!
Just for fun (as almost all assumptions are incorrect), assume:
- constant density r
- constant specific heat capacity c
- uniform temperature T(t)
- black body radiation
Then, thermal energy is (up to a constant) r•c•V•T(t) (where V is the volume) and radiated power is s•A•T(t)⁴ (where s is Stephan-Bolzmann constant and A is the area of the object).
Equating the loss of thermal energy with the radiated power:
r•c•V•(dT/dt) = -s•A•T⁴
This is a simple differential equation which provides T(t) :^) If I didn't mess up, the result is
T(t) = T(0)/[(1 + bt)^(1/3)]
where b = 3•s•A•T(0)³/(r•c•V).
Thanks for your kind words, I'm always happy to see your comments! I've just recorded another video today and hope to get it uploaded soon. Cooling of a black body is on my to-do list, this could of course become arbitrarily complicated but I was thinking of doing it using a simple model like the one proposed by the commenter above.
Sir after doing some analysis using the Stefan-Boltzmann law I found out that this model suggests that the intensity released by a star is proportional to the mass of the star raised to the power of 4 ! I find that quite interesting
Apparently, that is actually a pretty good approximation for Sun-like stars! See e.g. en.wikipedia.org/wiki/Mass%E2%80%93luminosity_relation
Sir I have been doing a lot of physics problems some of them are very hard where can I share the problems with you?
Feel free to email me at ben.yelverton@cantab.net!
@@DrBenYelverton ok
@@DrBenYelverton question sent
@@mxminecraft9410 Got it, looks interesting! I will have a go at solving it when I get the chance.
@@DrBenYelverton ok can you also upload a solution too?
👍🏼