At a constant temperature, the volume of a gas V is inversely proportional to its pressure P.
By what percentage will the pressure of the gas change if its volume increases by 25%?
Inversely proportional???  I have no idea of how to represent that
Inversely proportional question

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 16102016 14:48

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 16102016 14:51
(Original post by FizzleA)
At a constant temperature, the volume of a gas V is inversely proportional to its pressure P.
By what percentage will the pressure of the gas change if its volume increases by 25%?
Inversely proportional???  I have no idea of how to represent that
That is inversely proportional. 
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 16102016 14:53
"Inversely proportional" means that as one thing gets twice as big, the other thing gets twice as small, or if one thing gets ten times as big, the other thing gets ten times as small, etc.
Mathematically, if our things are x and y, then x is proportional to 1/y, or x = k (1/y), where k is some constant number (called the constant of proportionality).
In your case, the things are pressure and volume, so P = k (1/V), where k is some number. You don't need to know k to finish the question off! 
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 16102016 14:53
1.25V = K/P ???? 
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 16102016 14:56
(Original post by FizzleA)
How do I now solve the question? Do I work out K first?
1.25V = K/P ????
You should rewrite it as and then see what you can do the fraction on the right to get it into the form of where l will tell you the change in P.Last edited by RDKGames; 16102016 at 15:00. 
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 16102016 14:58
You don't need to work out k.
Rearrange the equation so that it says k = ...
You should now be able to write one equation for P and V before the change in volume and P and V after the change in volume.
Remember that k is constant, so it will be the same before and after the change in volume. Now solve your equations simultaneously. 
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 16102016 15:00
(Original post by Pangol)
"Inversely proportional" means that as one thing gets twice as big, the other thing gets twice as small, or if one thing gets ten times as big, the other thing gets ten times as small, etc.
Mathematically, if our things are x and y, then x is proportional to 1/y, or x = k (1/y), where k is some constant number (called the constant of proportionality).
In your case, the things are pressure and volume, so P = k (1/V), where k is some number. You don't need to know k to finish the question off!
V = K (1/P)
V increases by 25% to become 1.25V
1.25V = K (1.25/P) ??
Is this the answer, P also increases by 1.25 ?
I don't feel that that is correct because from your explanation earlier you said 'Inversely proportional' means "that as one thing gets twice as big, the other thing gets twice as small" ... so should P decrease by 25%? 
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 16102016 15:06
(Original post by RDKGames)
You don't need to know . You simply need to observe what happens to P as V increases by 25%.
You should rewrite it as and then see what you can do the fraction on the right to get it into the form of where l will tell you the change in P. 
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 16102016 15:09
(Original post by FizzleA)
How did you get it into the form 1.25V = K/lP ??
So
Apply the same idea here by dividing top and bottom by 1.25 and expressing the denominator as a decimal which should allow you to see the decrease in P. 
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 16102016 15:19
1.25V = 1.25K/P
I am aware that you can divide the numerator and denominator by the same number
1.25V = 1.25K/P
If I divide the fraction on the right by 1.25 then I get:
1.25V = K/1.25P ??Tagged: 
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 16102016 15:19
(Original post by FizzleA)
Thank you for explaining it.
V = K (1/P)
V increases by 25% to become 1.25V
1.25V = K (1.25/P) ??
Is this the answer, P also increases by 1.25 ?
I don't feel that that is correct because from your explanation earlier you said 'Inversely proportional' means "that as one thing gets twice as big, the other thing gets twice as small" ... so should P decrease by 25%?
If V has got 1.25 times larger, then P has got 1.25 times smaller.
What is P divided by 1,25? 
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 16102016 15:22
(Original post by FizzleA)
1.25V = 1.25K/P
I am aware that you can divide the numerator and denominator by the same number
1.25V = 1.25K/P
If I divide the fraction on the right by 1.25 then I get:
1.25V = K/1.25P ?? 
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 16102016 15:25
(Original post by Pangol)
You are correct when you say that this is not correct! But you have the right idea.
If V has got 1.25 times larger, then P has got 1.25 times smaller.
What is P divided by 1,25?
... So if I use V = k(1/P)
1.25V = 1.25k/P
1.25V = k/P/1.25...
k = 1.5625V / P  does this have any relevance?Tagged:Last edited by FizzleA; 16102016 at 15:32. 
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 16102016 15:28
(Original post by FizzleA)
= P/1.25 ?
... So if I use V = k(1/P)
1.25V = 1.25k(1/P)
1.25V = k(1/P/1.25)... 
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 16102016 15:31
(Original post by RDKGames)
Yes now turn P/1.25 into P multiplied by some decimal. So in other words, what is 1/1.25 as a decimal? 
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 16102016 15:32
(Original post by FizzleA)
0.8 ... therefore P will decrease by 20%? 
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 16102016 15:33
(Original post by FizzleA)
= P/1.25 ?
... So if I use V = k(1/P)
1.25V = 1.25k/P
1.25V = k/P/1.25...
k = 1.5625V / P  does this have any relevance? 
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 16102016 15:33
(Original post by RDKGames)
Precisely. 
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 16102016 15:37
(Original post by FizzleA)
0.8 ... therefore P will decrease by 20%? 
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 16102016 15:42
(Original post by Pangol)
Not exactly wrong, I think, but hugely and unecessarily overcomplicated. If you multiply V by 1.25, you have to divide P by 1.25. So the question is saying, what is the new pressure, in terms of the old pressure P, when this happens. The answer is P/1.25. But there is a slightly nicer way to write P/1.25, as P times something, rather than P divided by something,
V = k/P
1.25V = k/P/1.25
1.25V  k/1/1.25
1/1.25 = 0.8
A decrease of 20%Last edited by FizzleA; 16102016 at 15:43.
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