Room for B & J

Sir my doubt is why can't i simply use $V_1/T_1=V_2/T_2$. The question specify it follows an additional law , so it must be following the previous laws too.

John Rennie

6:04 AM

I think the point is that the pressure, volume and temperature are all changing at the same time.

In effect it's like an adiabatic process with $\gamma = 2$.

You know that for an adiabatic process we have $PV^\gamma = constant$? Yes?

Bhavay

@JohnRennie Sir actually no.... I mean i did study it , but i have to revise it and then solve problems from thermodynamics chapter.

John Rennie

If you take some volume V of gas and compress is adiabatically then all three of P, V and T change.

Bhavay

Should i circle back to this question when i have revised thermo ?

John Rennie

P increases while V decreases because the gas is being compressed, but because we are putting in work the temperature also goes up.

So you can't use e.g. Boyle's law because that assumes the temperature is constant, but here it is changing.

@Bhavay this question is much easier than you think and you don't need to revise anything to do it.

We are told that $PV^2 = const$, yes?

Bhavay

So the only thing constant is n.

John Rennie

6:09 AM

Yes. We'll assume $n = 1$ for convenience.

Bhavay

$PV/T=constant$

John Rennie

Yes, for an ideal gas it us always true that $PV = RT$

So that means $P = RT/V$, and we can use this to substitute for $P$ in $PV^2 = const$. Yes?

Bhavay

Aha, multiply by V and $VT=constant$

John Rennie

Yes :-)

Bhavay

but sir , how did you know that pressure is changing ?

(Other than experience )

John Rennie

6:11 AM

If $PV^2 = const$ and $V$ is changing that must mean $P$ is changing. Yes?

Bhavay

Ohh!

@JohnRennie Understood.

Next Q?

John Rennie

Yes

Bhavay

Q30 , A vertical ...(same page)

The problem i am facing is , that i don't think any mercury can be put over as then the piston move downwards due to unequal pressure.

John Rennie

Without any mercury the piston is at the top of the tube and the air in the tube is at atmospheric pressure. Yes?

Bhavay

Yes

$P_o=P_o$

John Rennie

6:16 AM

Now suppose we move the piston halfway down the tube i.e. we compress the air inside so the pressure is 2 atm (gauge pressure is 1 atm). OK so far?

Bhavay

yes. But then by that logic we can compress the air till the bottom by pouring more and more mercury.

John Rennie

Ah, but what you are forgetting is that the distance from the piston to the top of the tube is only 50cm, so we can't pour in more than 50cm of mercury.

And 50cm of mercury is only ⅔ of an atm. Yes?

Bhavay

@JohnRennie the length of tube is 100cm. Isn't the piston at top i.e at 100cm (initially)

So total mercury that can be poured = 100cm

John Rennie

Initially the piston is at the top so the distance of the piston from the top of the tube is zero. What I'm saying is that if we push the piston halfway down the distance from the piston to the top of the tube is now 50cm.

So we can now pour in 50cm of mercury.

Bhavay

But why till half ?

John Rennie

6:22 AM

When you have a problem like this it's often good to start with a trial calculation to see what happens, and that's what I am doing.

What I'm going to show you is that we cannot compress the piston to 50cm by puring in mercury.

Then I'm going to show you that we can compress it 10cm by pouring in mercury.

So somewhere in between there must be a maximum compression.

Once you understand this we can write the equation for x cm instaed of 50cm or 10cm, then solve for x.

Bhavay

Oh so 50cm = a trial number so to reduce the spectrum where the max value lie.

John Rennie

Yes, and to help understand the problem.

Bhavay

@JohnRennie i am using my pc.

John Rennie

The key point is that the mercury fills the space between the piston and the top of the column, and that restricts how much mercury we can add.

I can draw a diagram if it will help.

Bhavay

it is fine

John Rennie

6:26 AM

Suppose we compress the air column to a length $x$, i.e. the distance of the piston from the top of the column is $100-x$.

Then the maximum amount of mercury we can pour in is $100-x$ cm. Yes?

Bhavay

yes

sir wait.

John Rennie

So the pressure created by the mercury is $P_m = (100-x)/75$ atm.

Bhavay

@JohnRennie I remember trying this approach last night.

The problem that i faced was:

That , how can this be true $P_o +\rho g (100-x)=P_o$?

John Rennie

@Bhavay I don't understand how you got that equality.

Bhavay

The LHS = pressure exerted by Hg

Rhs =pressure by the other side of psiton

John Rennie

6:32 AM

Let's just use the gauge pressure i.e. the gauge pressure is $P - 1atm$.

75cm of mercury = 1atm, so $100-x$ cm of mercury is $(100-x)/75$ atm. Yes?

Bhavay

yes

John Rennie

Now the air in the cylinder was initially at 1 atm, and we compressed it from 100cm to $x$ cm, so the pressure inside the tube is now $100/x$ atm i.e. the gauge pressure is $P_a = 100/x - 1$

Bhavay

oh wait , I understood my mistake.

when the Air column is compressed , pressure is no longer $P_0$

John Rennie

Yes :-)

That should make the problem easy now.

Bhavay

I have another question.

John Rennie

6:37 AM

I have another question pending. Let me deal with that and I'll get back to you.

Bhavay

Okay , np.

John Rennie

@Bhavay ah, OK, satan29 says to answer your question first :-)

So what number is the question?

(oops that was you :-)

Bhavay

@JohnRennie Q34

I don't understand why i am getting the wrong answer.

The B means : Boyle's Law.(when tube is turned over)

I took everything in SI units.

The calculation is done by mathway, so i must be wrong in concepts somewhere.

John Rennie

So initially we have 45cm of air at each end at 1atm, and a 10cm plug of mercury separating the two (the mercury just behaves as a 10cm long sliding piston). Yes?

Bhavay

@JohnRennie Sir please go through my method first.

John Rennie

6:49 AM

How do you want to do this? Do you want to talk me through what you did? Or shall I say how I would solve it?

@Bhavay OK, you talk me through how you did it.

Bhavay

Initially the tube is turned upside down. I have shown it in the diagram and equated the net force =0

P1 is the pressure by lower side. Po=atm

Okay so far?

John Rennie

The tube isn't turned. It remains horizontal throughout.

Bhavay

@JohnRennie oops i meant question 33.

John Rennie

OK :-) I was confused for a moment :-)

Bhavay

@JohnRennie My apologies.

John Rennie

6:53 AM

OK, let's go. I find it really hard to read hand written notes so can you explain your calculation here?

Bhavay

The net force on the mercury column should be 0. I have just equated net force =0 and then calculated initial pressure in terms of Po.

John Rennie

The pressure at the bottom of the mercury column is $P_0 = 1$ atm, and the pressure change along a 10cm mercury column is 10/75 atm, so the pressure at the top of the mercury column is $P_{top} = 1 - 10/75$ atm.

Bhavay

Yes

@JohnRennie Although i did everything in si unit.

John Rennie

So the pressure of the air in the first step when the closed end is at the top is $P_1 = 65/75$ atm.

Bhavay

Can you also use SI units ?

John Rennie

6:58 AM

$P_1 = 65/75 \times 101325$ Pa

Yes?

Bhavay

Now use bolyes law

P2=P1*20/x

John Rennie

OK, you mean to find the volume the gas would have at 1 atm? I wouldn't do that yet ...

Bhavay

@JohnRennie no , when the tube is turned over.

John Rennie

I would use the same argument we just used to find the pressure when the tube is turned over. The pressure is going to be $P_2 = 1 + 10/75$ atm. Yes?

Bhavay

Yes , and P2=P1*20/x

Yes?

John Rennie

7:03 AM

Yes

$x = 20 \times P_1/P_2$

$$ x = 20 \frac{1 - 10/75}{1 + 10/75} $$

Bhavay

Does this equation make sense?

John Rennie

You have a sign wrong I think

Bhavay

Where?

John Rennie

$P_1 = 101325 - 13510$ and $P_2 = 101325 + 13510$. Yes?

Bhavay

Is it correct now?

John Rennie

7:08 AM

Yes, I think that's correct now.

Bhavay

@JohnRennie and i get x=15.2

But x should be 48

John Rennie

Verma gives the answer as 15cm. See page 38.

48cm is the answer to q35. Did you misread it?

Lol , i did.

:-)

Sorry i took 20 cm

7:12 AM

Yes :-)

Bhavay

Sir one more q?

John Rennie

Yes

Bhavay

Sir q35.

I am getting the wrong answer, I checked twice now!

Shall i explain my working ?

John Rennie

Yes, go ahead.

Bhavay

$76\times A\times 43= (76+20\sqrt3/2) \times A\times L$

John Rennie

7:19 AM

cos(60) = ½ not √3/2

Bhavay

Doesn't matter i did that too. It was not clear to me whether rotation of 60 was with vertical or horizontal

$76\times A\times 43= (76+20/2) \times A\times L$

John Rennie

Give me a moment to do the calculation ...

Bhavay

I get 38.

John Rennie

OK, I just did the calculation and got the correct answer. The tube is tiltedt 60° to the vertical so we use cos(60) = ½

Do you want to go through your calculation with this angle, or shall I go through mine?

Bhavay

2 mins ago, by Bhavay

$76\times A\times 43= (76+20/2) \times A\times L$

Is this correct ?

John Rennie

7:23 AM

No

Bhavay

I want to know why not

John Rennie

I don't understand your equation at all ...

You need to find $P_1$ and $P_2$ as in the last question then use Boyle's law. Yes?

Bhavay

Sir , I don't understand my equation either . But the instructor in a yt video does the question by that.

I was hoping you will understand it and then explain it to me. I can send the link of yt video of if u want.

John Rennie

I suggest we do the calculation our way, and see if we get anything like the instructor's equation. It may be a rearrangement that I don't recognise.

Bhavay

I want to do calculation in Hg.

Give me a moment to try it

John Rennie

7:30 AM

OK :-)

Bhavay

$PV=const$

When the tube is horizontal (assuming it is horizontal initially ) : $P_1V_1=76\times A\times 43$

John Rennie

The tube is vertical initially ...

Bhavay

Ohh

John Rennie

Bhavay

I am doing it here because I am lazy to do it in a nb. Plus i will bookmark it later whenever i want to review it again.

When tube is vertical : $P_1V_1=76\times A\times (43+20)$

John Rennie

7:36 AM

That doesn't look right ...

Bhavay

I see a problem too.

John Rennie

$P_1 = P_0(1 + 20/76)$. Yes?

($P_0 = 1$ atm)

Bhavay

or 76 cm of hg

$P_1V_1=(76+20)\times A\times (43+20)$

John Rennie

I don't get it. $V_1 = 43 \times A$

Bhavay

Isn't weight of 20cm hg also gonna act ?

John Rennie

7:40 AM

So $P_1 V_1 = P_0(1 + 20/76) \times 43 \times A$

$V_1$ is the volume of the air.

Bhavay

okay okay , i see my mistake.

John Rennie

We are going to apply Boyle's law to the volume of the air.

Bhavay

$P_2V_2=(76+10) \times A \times x$

Okay?

John Rennie

Yes

Bhavay

Voila!

John Rennie

7:44 AM

:-)

Bhavay

@JohnRennie Sir last question. A really small doubt.

John Rennie

Yes ... ?

Bhavay

In Q36 , why is pressure of both sides same?

John Rennie

It says the separator can slide freely. Yes?

Bhavay

yes

John Rennie

7:47 AM

So the net force on the separator must be zero, because if the net force was not zero the separator would slide until the net force was zero.

Bhavay

And sir will there be a difference in answer if the container was vertical instead of horizontal (This is not asked in the question)?

John Rennie

If the separator is massless then there will be no difference.

If the separator has a mass then there will be a difference, because now there must be a pressure difference between the top and bottom of the separator that supports its weight.

Bhavay

Okay , thanks . I have a class now.

John Rennie

OK, bye :-)

Bhavay

Bye . :-)

Bhavay

4:01 PM

@JohnRennie An equivalent command in windows would be "sudo shutdown -h +600"

John Rennie

@Bhavay Equivalent to shutdown /s /t 60 in Windows?

Bhavay

I want to log out/ shutdown my computer automatically .

In my laptop i would use that command ...

I tried using windows scheduler but it is asking for the script.

John Rennie

The way I always do stuff like this is to write a batch file. In fact I have a batch file to hand to do exactly this.

Bhavay

Would you care to share ?

John Rennie

rem ********************************************************************
rem ShutdownServer.bat
rem =================
rem ********************************************************************

set RBLOG=C:\temp\ShutdownServer.log

echo Starting ShutdownServer >%RBLOG%
date /t >>%RBLOG%
time /t >>%RBLOG%

shutdown.exe /s /t 0 1>>%RBLOG% 2>>&1

echo Finished RebootServer >>%RBLOG%
time /t >>%RBLOG%

This will shut the computer down, and it creates a log in the file C:\temp\ShutdownServer.log so you can check when the shutdown command ran.

Bhavay

4:07 PM

How can i tweak this too sleep?

Also, do I need to run this by scheduler ?

John Rennie

Let me check what the arguments for the shutdown command are ...

shutdown /h /t 0 does a hibernate instead of a shutdown.

So the script is the same but you just change the /s to /h

The way you do this is choose some convenient folder to keep script files e.g. in you Documents folder create a folder called Scripts and keep the script files in there. OK so far?

Bhavay

Yes

Can you wait for 5 minutes?

John Rennie

Yes, ping me when you want to pick this up.

Bhavay

@JohnRennie Hi

John Rennie

@Bhavay hi :-)

You'll need to tell Explorer to show suffixes otherwise you won't be able to create a file with the correct suffix.

Bhavay

4:17 PM

Sir do i need to save it in .batch ?

John Rennie

.bat not .batch

Bhavay

@JohnRennie You mean the browser ,as i use chrome.

John Rennie

No I did mean Explorer.

Bhavay

Just to clarify : Internet Explorer ?

John Rennie

No, the file explorer

This is where you tell it to show file extensions.

Bhavay

4:21 PM

John Rennie

Yes, that looks good.

Now right click it and choose Edit

Bhavay

okay , notepad opens up...

John Rennie

Yes, and you can copy my script and paste it in.

Bhavay

Done.

John Rennie

And change the /s to /h

Bhavay

4:24 PM

Also done.

John Rennie

There is one more thing to do. The script creates a log file in C:\temp\ShutdownServer.log, but I don't think the C:\temp folder exists by default.

So in the file explorer go to C:, right click and create a new folder called temp

Bhavay

Why would i need that temp file ?

John Rennie

When you're running things from the scheduler it can be very useful to have a log file showing what the scheduled command did.

Because you have no way of seeing what happened if, for example, the scheduled program didn't work.

Bhavay

Done.

John Rennie

Now you can test it by doubleclicking your new batch file, and it should make your PC hibernate.

Bhavay

4:27 PM

I didn't specify date , time.

John Rennie

What you've done is create a script that will hibernate your PC. The next step is to tell the scheduler when to run this script, but first let's check it works.

And the way you check it works is to run it manually now and check that it does indeed hobernate your PC.

Bhavay

Forgot to save , when i changed the s to h

But now it does nothing.

Earlier it was actually shutting down.

(I cancelled it )

John Rennie

Ah, for hiberation we don't need the /t 0. The line should be just:

shutdown.exe /h 1>>%RBLOG% 2>>&1

Bhavay

Worked like a charm.

John Rennie

:-)

Do we need to talk through creating the scheduled task? Or can you do it?

Bhavay

4:36 PM

I have never done it tbh .

John Rennie

OK, open the Task Scheduler

opened.

Done.

On the left click on Task Scheduler Library, then on the right click on Create Task

Bhavay

4:39 PM

Done.

John Rennie

Change the name to something descriptive e.g. Hibernate my PC

Done

Yes , done.

When do you want this to run?

At a specified time?

Bhavay

4:41 PM

I wanted to run this today before going to nap this afternoon .

John Rennie

Well the Task Scheduler is generally used for running tasks automatically under some predefined circumstances.

Bhavay

@JohnRennie Sir , you use windows 10 , but why are we config this for vista ?

John Rennie

@Bhavay that was just the default. I don't think it matters what you choose.

Anyhow, what should the conditions be for hibernating the PC?

At a set time? Or if you haven't used it for a time?

Bhavay

@JohnRennie Can we specify that if my chrome browser is on , only then run the script.

John Rennie

I'm not sure what you mean.

You mean if Chrome is the only app running?

Bhavay

4:46 PM

No .

If any app including chrome is running then run the script. If the chrome is not running then don't run the script.

John Rennie

These are the only conditions the Task Scheduler can use.

Bhavay

John Rennie

OK ... ?

Bhavay

I had a different screen.

I don't have the time option.

John Rennie

You are looking at a different tab. I showed the Triggers tab. That selects the conditions for the task to be triggered i.e. when the task starts.

Bhavay

4:51 PM

Oh got it.

John Rennie

The Conditions tab specifies some extra conditions for running the task.

It still isn't clear to me what you're trying to achieve ...

5 mins ago, by Bhavay

If any app including chrome is running then run the script. If the chrome is not running then don't run the script.

But apps will be running all the time.

Presumably you need some way for the task scheduler to tell when you've gone for a nap leaving the PC?

Bhavay

I have specified the time.

John Rennie

OK. Then go to the Actions tab and click New.

Bhavay

And then paste the script which saved.

John Rennie

Click the Browse button ...

Bhavay

4:55 PM

Done.

Pasted the location of the script.

John Rennie

Aha, OK.

That should be it then.

You've told the Task Scheduler to run your Hibernate script at a specified time.

Bhavay

Yes, Every monday 5.20pm

John Rennie

Just on Mondays? Not every day?

Bhavay

The truth is today i had a two hour long class on every Mondays (3.30pm-5.30pm) I wanted to go to sleep but If i slept i was sure that i would never be able to end my meeting. And if my lecturer saw me in the meeting after 5.30 pm he would ask me what are you doing after the class.. So you know...

(I hope u are not angry)

John Rennie

Angry? Why would I be angry?

Because you're trying to game the system? If so I heartily approve :-)

Bhavay

5:01 PM

You are helping a kid to bunk classes.

John Rennie

Whenever Satan29 has a boring lecture he starts asking me about relativity and quantum mechanics to pass the time :-)

Bhavay

You are a cool teacher. :-)

John Rennie