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A level math help.

I struggle with questions like these because I cant even tell what topic its from.
A manager of a company models the volume V of a gas as being inversely proportional to its pressure P. Some of this gas is stored in a cylindrical tank of radius 2. For safety reasons the gas is transferred to another cylindrical tank of the same height . Find the radius that this new tank will have to be so that the pressure of the gas is reduced by 84%

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Original post by mrwonderful
I struggle with questions like these because I cant even tell what topic its from.
A manager of a company models the volume V of a gas as being inversely proportional to its pressure P. Some of this gas is stored in a cylindrical tank of radius 2. For safety reasons the gas is transferred to another cylindrical tank of the same height . Find the radius that this new tank will have to be so that the pressure of the gas is reduced by 84%


It's a problem solving type - start by working through each sentence and expressing it mathematically.
V is inversely proportional to P so ...
Post your working
1553954190430182019934096255224.jpg
Original post by Muttley79
It's a problem solving type - start by working through each sentence and expressing it mathematically.
V is inversely proportional to P so ...
Post your working
Original post by mrwonderful
1553954190430182019934096255224.jpg


You haven't introduced a new radius yet ...
(edited 5 years ago)
Original post by Muttley79
You haven't introduced a new radius yet ... Volume of gas remains the same.

Doesn't the volume increase to lower the pressure?
Original post by RogerOxon
Doesn't the volume increase to lower the pressure?


Edited - too busy cooking - they haven't found k from original is what I meant.
Reply 6
This question is part of the CGP practice papers. Students I give it to struggle because they assume it must involve calculus and that assumption leads them astray. It's actually a question that only requires GCSE knowledge and it's a bit strange to include it in an A Level paper.
Original post by mrwonderful
I struggle with questions like these because I cant even tell what topic its from.
A manager of a company models the volume V of a gas as being inversely proportional to its pressure P. Some of this gas is stored in a cylindrical tank of radius 2. For safety reasons the gas is transferred to another cylindrical tank of the same height . Find the radius that this new tank will have to be so that the pressure of the gas is reduced by 84%

You've got a good start, but need to be careful not to confuse symbols for the same property between the two vessels. I'd work-out the ratio of volumes first, before starting a second equation in terms of radii, so as to keep the equations simpler.

V1PV \propto \frac{1}{P}

V2V1=P1P2\therefore \frac{V_{2}}{V_{1}}=\frac{P_{1}}{P_{2}}

V2=V1P1P2\therefore V_{2}=V_{1} \frac{P_{1}}{P_{2}}

You already correctly deduced that P2=0.16P1P_{2}=0.16 P_{1}
(edited 5 years ago)
Reply 8
Original post by RogerOxon
You've got a good start, but need to be careful not to confuse symbols for the same property between the two vessels. I'd work-out the ratio of volumes first, before starting a second equation in terms of radii, so as to keep the equations simpler.

V1PV \propto \frac{1}{P}

VcylinderVsphere=PspherePcylinder\therefore \frac{V_{cylinder}}{V_{sphere}}=\frac{P_{sphere}}{P_{cylinder}}

Vcylinder=VspherePspherePcylinder\therefore V_{cylinder}=V_{sphere} \frac{P_{sphere}}{P_{cylinder}}

You already correctly deduced that Pcylinder=0.16PsphereP_{cylinder}=0.16 P_{sphere}

I’m not sure why your working includes spheres?
Original post by Notnek
I’m not sure why your working includes spheres?

Thanks - I've corrected it. I'd only just woken up, apparently not completely ..
I tried my best. Could u check it.
Original post by Muttley79
You haven't introduced a new radius yet ...


20190330_145840.jpg
I agree. But because of the new spec its hard to get realistic papers.
Original post by Notnek
This question is part of the CGP practice papers. Students I give it to struggle because they assume it must involve calculus and that assumption leads them astray. It's actually a question that only requires GCSE knowledge and it's a bit strange to include it in an A Level paper.
Reply 12
Original post by mrwonderful
I agree. But because of the new spec its hard to get realistic papers.

CGP papers are great for the new spec. It's just this question which is slightly odd.

In addition to the mock/practice/past papers provided by your teacher, also try the specimen papers from other exam boards since the content is the same (just ignore any questions related to the large data set).
Reply 13
Original post by mrwonderful
I tried my best. Could u check it.


20190330_145840.jpg

This isn't correct. If you're going to do it like this then I recommend getting your equation in terms of P:

P=kπr2h\displaystyle P=\frac{k}{\pi r^2 h}

Then in the first tank the pressure is P=k4πhP=\frac{k}{4\pi h}

Then work out how the radius changes if P0.16PP\rightarrow 0.16P.

But as shown above you can just do this question using a proportionality argument and you can ignore the constants π\pi, kk and hh.
Original post by mrwonderful
I agree. But because of the new spec its hard to get realistic papers.

I think a 'better' approach is to remember PV for both is the same as both = k
You know the new P = 0.16 x old P so use that.

Exam boards have produced loads of resources - has your teacher not given you loads of practice papers?.
Original post by Muttley79
I think a 'better' approach is to remember PV for both is the same as both = k
You know the new P = 0.16 x old P so use that.

Exam boards have produced loads of resources - has your teacher not given you loads of practice papers?.


i got 3.3 as the radius. we have only gotten 2 full papers to practice. he keeps saying there arent many out there.
Reply 16
Original post by mrwonderful
i got 3.3 as the radius. we have only gotten 2 full papers to practice. he keeps saying there arent many out there.

That's not right. Please post your working.

In my opinion the simplest way to do this question is a simple proportionality argument which ignores all the constants:

v1pv \propto \frac{1}{p}

vr2v\propto r^2 (since π,h\pi, h are constant)

1pr2\Rightarrow \frac{1}{p} \propto r^2

r1p\Rightarrow r \propto \frac{1}{\sqrt{p}}

So if pp multiplies by 0.16 then it should be clear what rr must multiply by.
Original post by mrwonderful
i got 3.3 as the radius. we have only gotten 2 full papers to practice. he keeps saying there arent many out there.

It should be an expression in terms of the old r - can you post what you have?

Are you doing Edexcel? We've had a lot of resources via the [locked but available to teachers] Emporium.
Original post by Notnek
That's not right. Please post your working.

In my opinion the simplest way to do this question is a simple proportionality argument which ignores all the constants:

v1pv \propto \frac{1}{p}

vr2v\propto r^2 (since π,h\pi, h are constant)

1pr2\Rightarrow \frac{1}{p} \propto r^2

r1p\Rightarrow r \propto \frac{1}{\sqrt{p}}

So if pp multiplies by 0.16 then it should be clear what rr must multiply by.

I find most students prefer not to work with the proportional sign - so I got r^2 = 0.16R^2 where r is original radius and R the new
Reply 19
Original post by Muttley79
I find most students prefer not to work with the proportional sign - so I got r^2 = 0.16R^2 where r is original radius and R the new

That's because it's not encouraged at GCSE which is a shame. You get questions in GCSE exams like "if this variable doubles, what happens to this variable?", which should be a very simple proportionality argument but students often struggle or resort to algebra when there's no need.

I would expect a Physics student to be very confident with this kind of argument.

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