@user586228 my bad :-). Because I couldnt comprehend those notation lol :D

@ManasDogra It looks like you are expected to identify it to be a carnot cycle

Please, how can I calculate a tetrad basis for a given non-diagonal metric tensor?

@ManasDogra I have no idea how to read F:U graphs I'm afraid. In fact I don't think I have ever seen one before you asked.

@RobinSingh Hi Robin :-)

What does angle of friction mean? Isn't friction always parallel to the surface?

@user586228 that's suspiciously close to the reciprocal of Avagadro's number ...

@JohnRennie ncert defines is as the angle between I think Normal reaction and Frictional force

or the reciprocal

@RishiNandhaVanchi I must admit I have never encountered the term.

its really confusing where the theta i defined im scrolling through the book to see how it was defined

i dont find it useful either, its just there so they can ask us a question for one mark

@RishiNandhaVanchi i got B , but the 3/2 is over T and not V.

oh yeah

I switched T and V while writing final ans for some reason

and marked B

maybe thats why the question is deleted.

no answer is matching

yeah got it thanks

@RobinSingh yes, what is answer given?

@JohnRennie Sir, angle of friction is probably just a useless term. It is defined as the angle made between the normal reaction force and the resultant force of normal reaction force and friction.

@Rover Wsin(theta)

@RobinSingh askiitians.com/forums/Mechanics/… see second answer ...

Yeah I saw that already but we are given a horizontal plane in the question whereas they kept in on an inclined plane

@RobinSingh Yes.. , then can't say anything may be ans given is incorrect.

Sir, maybe you have heard of Angle of Repose. I think both are same. This is angle of friction as defined by Wikipedia

@Rover I think so too

@RobinSingh it looks to me as if W tanθ is correct.

Because tanθ = μ and the frictional force is Wμ

Yes sir that's what I thought too

So, the given answer is wrong?

@RobinSingh I'd have to see exactly what the question said to comment. Can you post a picture of the question?

It came in a test, the solution is kind of confusing. I think the psi is angle of incline

But it says the plane is horizontal, so ψ = 0°

Yes sir, but i think they are trying to create an angle of inclination and then they calculated what is the force on the body along the incline when the body just starts to move. This should be wrong.

I think it's a misprint.

The question and the solution don't match.

Yes sir

I think so too

I think I will contact with my teacher

Thanks :-)

they probably assumed an angle psi between F and surface

@JohnRennieCan you describe the analogy like you said close to the avogaro's number

Why is the analogy?

@RishiNandhaVanchi Just like that? F=U-TS afterall !!!

@ManasDogra im not aware of how F=U-TS is defined, but most of the times we are only given carnot under disguise :-)

theres another reason you cant be given WACKO processes

within a segment heat need not just be gained by the system

efficiency is defined a w/Qabsorbed. which isnt Qnet

so like say you have a straight line in PV, even if its an expansion, its would absorb some heat, emit some in between and absorb more

I believe we'll have to follow strategies like integrating along adiabatic components and stuff which gets really involving

@ManasDogra prnt.sc/xjudv3

It is a good idea to check if a cycle is carnot or not since we can shorten the process much faster.

@RishiNandhaVanchi Most qns I have encountered are polytropic, hopefully they don't get any crazier ideas.. . .

hehe lol

kvpy did have one question along these lines

ill see if I can find it

it was qualitative though

they gave a process that was a triangle in PV. options were equalities and inequalities involving efficiency

there was an exponential type of relation in kvpy past year papers too. And truthfully I found out by integrating and got the exact exp however the approximation seemed kinda bogus

let me see if I can find that

the one i sent above?

I was skimming past it they have alloted me bonus for this one

unofficial solutions they release for kvpy are mehhh tbh they seem to work backwards from answer key

is there an official solution for kvpy?

yeah they typoed and switched TV i think. Because we got B except T and V switched

there isnt

prnt.sc/xjut8z

@RishiNandhaVanchi that was what I remember about it.

I learned one thing that in kvpy u need to qualitatively attach it first lol

that was the qn I was talking about

I still don't get the solution though

do we have spoilering features here?

like ||this||

no

>! testing >!

ok nope

prnt.sc/xjuy1n <- solution

im gonna first rewrite it into T and V and then see what happens at large T

might need to differentiate

wait the solution give pressure compressibility right?

we need thermal compresibility?

Yes you will have to do exactly that. All of it makes sense until they just left P in the last step

ive seen unofficial solutions go wrong

take a look at the solution it is a terrible amount of differentiation

@RishiNandhaVanchi :(

you can skip a lot of the ugliness by carefully cancelling terms in differentiation

actually the value of compressibilty depends on the exponential of T, I just did it again

hopefully my mspainting is readable

at last step im put V^2/3 again

V^2/3 = c/T e^-kT

so at T-> inf you get constant compressibility

@RishiNandhaVanchi for compressibility we must replace $dT$ with $dP$

for thermal compressibility too?

wait what is thermal compressibility

I only know one compressibility I read in thermodynamics and that has the replacement I mentioned

and a -ve sign

I think you meant isothermal compressibility in question?

it is the inverse of bulk modulus

ohh okok

i thought thermal compressibility was defined as dV/VdT for some reason

is there a term like that?

i googled and got none

its just me guessing term definitions because of dx memory

@napstablook and T is large

@RishiNandhaVanchi prnt.sc/xjw32c

This was the end result of my estimation , I don't get where I went wrong :(

e^PV/E was in the lhs

so e^-PV/E in rhs

(speaking with respected to original equations given)

yep

uve taken in rhs guess thats where

and its not proportional to T^-2

the word proportional applies only when no other term in T is there

xe^x proportional to x is false

@RishiNandhaVanchi I know but the options don't even address that. . .

they do

when you take e^PV/E

at infinity that terms becomes really really small

that term becomes infinitely large right? PV=RT

nono its not e^positive x

oh I get it, my allen test papers have errors in it. It missed the negative in expo

I have this doubt with how excitation states are numbered if more than one electrons are there in the system

ive been searching in google but couldnt get a lot

i get that electron at highest energy level goes to one higher -> first exitation state

dont get the second

@RishiNandhaVanchi I know this is a JEE chat room..but, actually this question is from postgraduate entrance exam, so you know...all kinds of things come there :)

I believe PHOs cover thermodynamics to this depth

there was one question which gave U in terms of S,T and something i think

some state functions like A or F which i had no idea of

@napstablook The definition you used is for Gibb's Free energy, not Helmholtz free energy..

@RishiNandhaVanchi Yes I remember doing that one.

@ManasDogra and we got the same answer because it just became like U with a different coefficient

which one?

@ManasDogra yeah sorry, my bad.

PROBABILITY RIGHT?

sorry for caps

no i mean

if I am told the atom Mg is at second excitation state

what state is it at