Problem Solving Strategies

5:13 AM

Q1- I cannot equate the initial and final mechanical energy after a time interval dt bcoz the table is doing negative work on the chain. Is this correct?

Q2- If I were to write the acceleration of the chain as vdv/ds then what exactly is s here and how is it related to x which is the length of the chain inside the tube?

I think I wrote Q1 wrong. Here- Is the table also doing negative work on the chain?

EVO

6:26 AM

@JohnRennie Sir are you free

John Rennie

@EVO hi :-)

@EVO yes, I'm free.

EVO

Sir why is the avg kinetic energy of a gas molecule given by 3/2 KT and not F/2KT

f- degrees of freedom

John Rennie

For an ideal gas F = 3, so ³⁄₂ and F/3 are the same thing.

EVO

So isn't there anything like an ideal diatomic gas where the interaction is only between 2 atoms

John Rennie

An ideal diatomic gas has 3 degrees of freedom for motion, 2 DOFs for rotation and 1 DOF for vibration. Yes?

EVO

6:32 AM

yes

Srijan M.T

@EVO Check this. Maybe it will help.

John Rennie

The 3 DOFs of motion are associated with the linear kinetic energy, the two rotational DOFs are associated with the rotational kinetic energy and the 1 vibrational DOF is associated with the vibrational energy.

Srijan M.T

This is what my teacher told me. @JohnRennie Pls continue sir. Just a bit sharing if it helps.

John Rennie

So to an extent it is a matter of terminology. If we are considering only linear motion then we have three DOFs and the KE is ³⁄₂kT.

EVO

@SrijanM.T Thanks.@JohnRennie my real question is this statement "The average kinetic energy of gas particles is proportional to the absolute temperature of the gas, and all gases at the same temperature have the same average kinetic energy.
". Isn't this false

John Rennie

6:35 AM

@EVO no that's true.

Can you clarify why you think it might be false?

EVO

Shouldn't they mention the type of gas

John Rennie

No, it's true for all gases.

Polyatomic gases have extra energy because they have rotational and vibrational energy.

But if we consider just the linear KE then all types of gas have the same linear KE i.e. ³⁄₂kT.

EVO

But when we say K.E dosent it include the translational and ROTational K.E(FOr polyatomic gases)

John Rennie

No, KE normally just means the translational energy

It does not include the rotational or vibrational energy.

EVO

@JohnRennie oh i didn't know that. Thanks sir

John Rennie

6:40 AM

You're welcome :-)

EVO

@JohnRennie does this apply only ifor gases, I mean the K.E for a rolling ball is K.E(rot) +K.E(trans) right?

John Rennie

I'm not sure there is a universally accepted standard for this. Speaking personally, to me KE always means translational KE unless the text specifically states otherwise. If I was going to include vibrational and rotational KE I would say total energy.

For example if talked about the KE of a cricket ball we would mean ¹⁄₂mv² and we wouldn't include the energy of all the vibrating molecules in the cricket ball.

EVO

@ OK sir

John Rennie

If you're doing a JEE question the question will normally make clear whether you should include rotational and vibrational energy.

RishiNandha Vanchi

7:01 AM

@RobinSingh one thing I used to miss is how there's normal force by the corner of the table

which doesnt contribute to friction

@RobinSingh yeah we cant directly conserve energy

But we can write a = vdv/ds along the chain

@RobinSingh ds by how we are writing the equations is gonna be small displacement of chain to right/ downwards

which is = dx

sorry wait

I thought you meant h by x

x is a coefficient

vdv = hg da / (l-a)

satan 29

i think the chain segments are going to get piled up

and not spread linearly like in your drawin

g

RishiNandha Vanchi

7:24 AM

yeah, I drew it like that so I can mark a

doesnt affect the analysis right?

unless we are getting very realistic

satan 29

i mean the way i am picturing the situation, a is zero...

Robin Singh

I think he just wants a variable to measure the length of the length pf the chain that’s in air

@RishiNandhaVanchi I didn’t get what you said here. What do you mean by “by the corner of the table “?

I know you’re referring to a different problem (coz friction is 0 here)

@JohnRennie Hello sir :-)

Just stating my questions again-

If I were to write the acceleration of the chain as vdv/ds then what exactly is s here and how is it related to x which is the length of the chain inside the tube?

John Rennie

7:49 AM

Hmm, I'll have to think about this one.

John Rennie

8:14 AM

@RobinSingh I got:

$$ \frac{d^2x}{dt^2} = - \frac{hg}{x + h} $$

Srijan M.T

8:28 AM

For Charles law , can I say that at counts at temperature and no of moles of a given gas , volume and pressure will not change @JohnRennie

John Rennie

Charles law states that at constant pressure volume is proportional to temperature i.e. the ratio T/V is a constant. Yes?

Srijan M.T

Yes

@JohnRennie We know PV=nRT. So , does it also depend on n?

John Rennie

So V = constant x T.
if you hold the temperature constant that means V must be constant.

Srijan M.T

@JohnRennie Yes

John Rennie

@SrijanM.T yes, it does depend on n.

Srijan M.T

8:33 AM

Ohk.

John Rennie

Though n is normally constant.

Srijan M.T

Also , if I say in a container. V1 of container = 100mL , and temp = 300. So , V and T is given but not P. Then , Shall I say P1 = 3 atm ?

Since PV/T= constant

John Rennie

You need to know n. You can't calculate the pressure without knowing n.

Srijan M.T

Then we will to have PV=nRT

Then only we can find ?

If I say n = 2

Then , value of P would be in decimal is my confusion because of value of R

John Rennie

I'm not sure what you are asking.

P = nRT/V

So to find P you need to know T, V and n

Srijan M.T

8:38 AM

Yes. I told T= 300K

V=100mL

and n = 2

So , if I now find P. It should be in decimal points because of of the value of R=8.314

John Rennie

Then P = 6000R

Srijan M.T

Or 0.821 depending on units

Then , I get 49.884*1000

If I take R=8.314

John Rennie

No, wait, hang on. Lets use SI units.

Srijan M.T

Ohk.

John Rennie

100mL = 0.1L = 0.0001 m³. Yes?

Srijan M.T

8:41 AM

Yes

John Rennie

So P = 2 x 8.314 x 300 / 0.0001 = 49884000 Pa

Srijan M.T

Ohk.

John Rennie

= 492 atmospheres

Srijan M.T

Ohk. So , that’s how I would do it.Thanks a

lot

John Rennie

:-)

Srijan M.T

9:16 AM

For this graph , can I say that as volume increases of a gas , pressure decreases

Then , if T increases , then P and V both increases ?

John Rennie

PV = nRT. Yes?

So the product PV increases as T increases.

Srijan M.T

Yes

ohk.About individual term if we talk , then P and V increase , if T increase

Also , looking at one line I,e 200K. So , if T is const , then as V increase , P decrease ?

John Rennie

Yes, because at constant temp P is proportional to 1/V

Srijan M.T

Ohk.

Thanks sir.

satan 29

@JohnRennie sir how

John Rennie

9:24 AM

@satan29 consider the tension at the top of the vertical section of the chain.

satan 29

ok

John Rennie

the weight of the chain hanging below this point is $\lambda h g$ where $\lambda$ is the linear density ($\lambda$ is going to cancel out of the final expression).

satan 29

yes

John Rennie

The net downward force on the vertical bit of the chain is the weight minus the tension, so we get:

$$\lambda h g - T = \lambda h a$$

satan 29

oh and T accelerates the horizontal part with the same acceleration a

John Rennie

9:27 AM

where $a$ is the downwards acceleration of the vertical bit of the chain.

Yes :-)

satan 29

ah yes indeed

John Rennie

And the equation I gave drops out.

satan 29

but wait, what is x

John Rennie

$x$ is the length of the chain in the horizontal part of the tube i.e. at time zero $x = L - h$ and when the last bit of the chain leaves the horizontal tube $x = 0$.

So the mass of the chain in the tube is $m = \lambda x$.

Then we get $T = \lambda x a$

satan 29

yes

and a is the rate at which x decreases

John Rennie

9:32 AM

Yes. The acceleration is the same for the whole chain. Substitute for $T$ in the first equation and you get the equation I cited.

satan 29

yes. Then writing d^2x/dt^2 as vdv/dx, we get $v=\sqrt{2ghln(l/h)}$

limits of x are l-h to 0

@RishiNandhaVanchi you are correct inffact

your acceleration is -d^2/dt^2( l-a-h) which is d^2a/dt^2= vdv/da

and your limits of a will be a to l-h

Srijan M.T

9:52 AM

Sir , I Checked about this law to calculate pressure of a dry gas. So , Aqueous tension means when water is evaporated , the pressure exerted by water vapour is aqueous tension. Then , Let us say in a container there are 3 gases (Not sure if different or same gas) which exert partial pressure or pressure total = P1+p2 +p3 . Then , to calculate pressure exerted by a dry gas(a gas which has no amount of water vapour in it) = p(total) - aqueous tension = total dry gas pressure of all 3 gases.

So , it says online that dry gas is a gas which has a little amount of methane in it. An example is CO2. So , I am wondering what does dry gas actually mean in terms of its composition ?

So , I want to confirm whether what I wrote is right or not and what does dry gas compose of ?

John Rennie

I have never heard the expressions aqueous tension or dry gas. They sound like engineering terms rather than physics.

Srijan M.T

10:22 AM

Ohk.

Image on the right talks about dry gas and aqueous tension.

John Rennie

OK I know that as vapour pressure.

Srijan M.T

K. Can you help me in it pls. I am not able to get it

John Rennie

I need to go I'm afraid. I'll be around tomorrow as usual.

Srijan M.T

Sure sir

Np

RishiNandha Vanchi

12:15 PM

@satan29 yeah the catch was understanding that normal force would just "prevent an object from moving through a surface", nothing more, nothing less

the object here is the length of chain that's on ground

@SrijanM.T thats just partial pressure of H2O in air

Srijan M.T

@RishiNandhaVanchi hmm but what’s the deal with dry gas and aqueous tension

RishiNandha Vanchi

12:43 PM

i dont get your doubt

partial P of gases other than H2O defined to be partial pressure of dry gas

partial P of H2) defined to be aqueous tension

Srijan M.T

1:40 PM

@RishiNandhaVanchi My teacher told me steam as aqueous tension meaning

I Checked about this law to calculate pressure of a dry gas. So , Aqueous tension means when water is evaporated , the pressure exerted by water vapour is aqueous tension. Then , Let us say in a container there are 3 gases (Not sure if different or same gas) which exert partial pressure or pressure total = P1+p2 +p3 . Then , to calculate pressure exerted by a dry gas(a gas which has no amount of water vapour in it) = p(total) - aqueous tension = total dry gas pressure of all 3 gases.
So , it says online that dry gas is a gas which has a little amount of methane in it. An example is CO2. So …

I Hope this helps you to understand my doubt

RishiNandha Vanchi

"dry gas" that the book refers to is just gas without H2O

online's probably refering to some other dry gas

Srijan M.T

@RishiNandhaVanchi Is it even possible to have it. Like

RishiNandha Vanchi

??

Srijan M.T

So , if I have neon , argon and oxygen as ptotal

RishiNandha Vanchi

then aqueous tension = 0

Srijan M.T

1:52 PM

Ohk.

So , like best example is steam

for subtracting a aqueous tension

RishiNandha Vanchi

aqueous tension is a pretty useless term theoritically speaking. they are defining it for a realistic context of how there's humidity everywhere

Srijan M.T

@RishiNandhaVanchi ohk. I feel it’s not even imp for JEE Q then ?

RishiNandha Vanchi

@SrijanM.T Ptotal = aq tension because its all H2O now and nothing else

Srijan M.T

@RishiNandhaVanchi So , dry gas for this condition means empty space ?

RishiNandha Vanchi

@SrijanM.T For main they might ask you definition based, mains is like everything ncert

Srijan M.T

1:54 PM

@RishiNandhaVanchi Ohk

RishiNandha Vanchi

for advanced I wouldnt expect a ques on aq tension out of everything else

@SrijanM.T yeah

Srijan M.T

So , mains is easy right ?

Many tell me that 75Q are more than enough time (3hrs) to be solved in mains

RishiNandha Vanchi

depends lol

past mains I used to be short of time

but on the day of mains I had like 45 min to spare

it becomes more about how competant you are than dificulty

Srijan M.T

2:19 PM

@RishiNandhaVanchi Hmm

K 🤔

CHEMOJEE

3:31 PM

Could anyone help me with problem 29 ?

Srijan M.T

4:44 PM

To solve a Q based on gas laws. When taking R=8.314. The units should be L , atm , K ?

Rover

@CHEMOJEE 11m ?

CHEMOJEE

5:04 PM

@Rover 8.1

Srijan M.T

5:15 PM

Guys , if transition for molecules happens from high pressure to low pressure. Then , is it also that it happens form low volume to high , high temp to low temp

Robin Singh

@SrijanM.T No, the SI units should be used here

@SrijanM.T not necessarily

Srijan M.T

Ohk.@RobinSingh

@RobinSingh Which one of mine is wrong

Rover

@SrijanM.T depends on question, basically R has units same as work done.

Are you asking units for R=8.314 ?

It can be J$K^{-1}mol^{-1}$

user435118

5:33 PM

If the point of radioactive decay is to make a nucleus more stable by reducing the number of neutrons compared to the number of protons what is the point of beta+ decay if the opposite occurs?

Srijan M.T

@Rover KK

Transcript for

Problem Solving Strategies