## gas law problems..

**Anonymous**

hey..just started on gas laws..

according to boyle's law

p = k1/v

(p is inversely proportional to v)

according to pressure law..

p= k2T

(p is proportional to T)

so combining these equations..it would seem that

T= k1*k2 v/T

= k3 V/T

which means T is inversely proportional to v, which is all wrong! as charles law says T is proportional to V

can anyone tell me why this is wrong?

banizavanessa (not verified)| 14 October 2007 - 10:33am## what do you mean bySTP?

what do you mean bySTP?

banizavanessa (not verified)| 13 October 2007 - 6:49am## so in boyle's law the

so in boyle's law

the constant there is temperature?

banizavanessa (not verified)| 13 October 2007 - 6:52am## ahuh..... yeah i got

ahuh.....

yeah

i got

it

thnks

Martin17| 11 April 2006 - 10:41amp= kt and p=K/V; therefore p =kKt/V or p =kt/V solving for t = pV/k; you just don't know how to add.

Anonymous| 12 April 2006 - 8:32am[quote="Martin17"]p= kt and p=K/V; therefore p =kKt/V or p =kt/V solving for t = pV/k; you just don't know how to add.[/quote]

I've never been able to work this out, since I first came across it in A levels.

Surely your answer is wrong though:

if p=kT and p=K/V, then kKT/V, which is kT*K/V, which is P*P, is p²? Admittedly, at P is a constant in Charles' Law, this doesn't matter, and you still get that T is proportional to V at fixed p. It just doesn't seem a mathematically acceptable way of doing it.

I've just always depended on pV=NkT to work it all out :oops:

Martin17| 13 April 2006 - 9:21amBoyle's Law states that the volume of an ideal gas is inversely propostional to pressure; that is volume is equal to some constant (k) divided by pressure; thus V=k/P.

Charles' Law states that the volume of an ideal gas is directly proportional to temperature; that is volume is equal to some constant (K) times temperature; V=KT.

ADDING these laws gives 2V = kKT/P; dividing by 2 we get V = kKT/2P; subsuming the combined constants, kK/2, for a single gas constant, R, we get V=RT/P, which is the classic gas law.

To solve for P we multiply both sides of the equation by P and get

PV = RT

divide by P and get

P = RT/V, that is pressure equals the gas constant time temperature divided by pressure.

I don't see why when adding the equations you would expect to get P-squared. I think the math is pretty straight forward, even for someone as benighted as I. :)

Anonymous| 14 April 2006 - 12:40pm[quote="Martin17"]Boyle's Law states that the volume of an ideal gas is inversely propostional to pressure; that is volume is equal to some constant (k) divided by pressure; thus V=k/P.

Charles' Law states that the volume of an ideal gas is directly proportional to temperature; that is volume is equal to some constant (K) times temperature; V=KT.

ADDING these laws gives 2V = kKT/P; dividing by 2 we get V = kKT/2P; subsuming the combined constants, kK/2, for a single gas constant, R, we get V=RT/P, which is the classic gas law.

To solve for P we multiply both sides of the equation by P and get

PV = RT

divide by P and get

P = RT/V, that is pressure equals the gas constant time temperature divided by pressure.

I don't see why when adding the equations you would expect to get P-squared. I think the math is pretty straight forward, even for someone as benighted as I. :)[/quote]

I was saying you should get p² because you have [i]multiplied[/i] the two equations together.

V = k/p

V=KT

Adding these: v + v = 2V = KT + k/p -----not what you stated

Multiplying these: v*v = v² = KkT/p -----what you stated, but not 2v!

So I *think* you are muddling two things up, and neither of them furnishes the desired answer.

Martin17| 15 April 2006 - 5:17amI am adding. Here are all the steps in the process.

Charles' and Boyle's Law give us 1a) V=k/P and 1b) V=KT where V is volume, P is pressure, T is temperature and k and K are undefined constants associated with the changes in volumes caused by pressure and temperature respectively.

adding we get

2) 2V = k/P + KT, multiplying both sides of the equation we get

3) 2VP = k + KTP

however by 1a V+k/P; therefore, k = VP; thus,

4) 2VP = VP + KTP; hence

5) VP = KTP; however by 1a V=k/P; therefore PV=k; therefore P=k/V; hence

6) VP = KTk/V or VP = kKT/V; hence

7) P = kKT/V[sup]2[/sup]

if we define kK/V as the gas constant we have

8) kK/V = R; thus, 7) becomes

9) P = RT/V; hence

10) VP = RT and solving for V we get

11) V = RT/P that is volume is directly proportional to temperature and inversely proportional to pressure, which is the empirical situation with gasses.

I'm not sure who is responsible for step 8) nor why R was chosen to symbolize the product of temperature and pressure constants divided by volume, but that is how the law was derived. At some later time R was replaced in textbooks by C or K for reasons unknown to me so I've seen 11) given as V = KT/P or V = CT/P.

Anonymous| 15 April 2006 - 9:16am[quote="Martin17"]I am adding. Here are all the steps in the process.

Charles' and Boyle's Law give us 1a) V=k/P and 1b) V=KT where V is volume, P is pressure, T is temperature and k and K are undefined constants associated with the changes in volumes caused by pressure and temperature respectively.

adding we get

2) 2V = k/P + KT, multiplying both sides of the equation we get

3) 2VP = k + KTP

however by 1a V+k/P; therefore, k = VP; thus,

4) 2VP = VP + KTP; hence

5) VP = KTP; however by 1a V=k/P; therefore PV=k; therefore P=k/V; hence

6) VP = KTk/V or VP = kKT/V; hence

7) P = kKT/V[sup]2[/sup]

if we define kK/V as the gas constant we have

8) kK/V = R; thus, 7) becomes

9) P = RT/V; hence

10) VP = RT and solving for V we get

11) V = RT/P that is volume is directly proportional to temperature and inversely proportional to pressure, which is the empirical situation with gasses.

I'm not sure who is responsible for step 8) nor why R was chosen to symbolize the product of temperature and pressure constants divided by volume, but that is how the law was derived. At some later time R was replaced in textbooks by C or K for reasons unknown to me so I've seen 11) given as V = KT/P or V = CT/P.[/quote]

That's all well and good, [b]but[/b], you are defining R to be a function of V, but V is surely a variable, so the constant cannot be constant! I can't see how it can be acceptable to go any further than step 7) by that.

Also, I dunno about using C, but k (or k[size=8]B[/size]) is the boltzmann constant. That is used for pV=NkT, where N is the number of *atoms*, as opposed to pV=nRT, where n is the number of *moles*.

But you probably already knew that.

How the badger can R be inversly proportional to Volume?! [img]http://forums.webelements.info/images/smiles/icon_confused.gif[/img]