Using Ideal Gas Law and Charles Law to compute limit

[Torshi]

Homework Statement

The ideal gas law from chem is PV = nRT. A process carried out at const. pressure is said to be isobaric. A process carried out at const. temperature is said to be isothermal.

A.) Using limits and the ideal gas law and assuming const. number of moles, show that that the volume of gas in an isobaric process goes to 0 as temperature goes to 0 and that the volume of gas in an isobaric process goes to +∞ as temperature goes to +∞. (Note: this is related to Charles' Law)

Homework Equations

PV=nRT
Charles Law: V1/T1 = V2/T2 or V2/V1 = T2/T1 or V1T2 = V2T1

The Attempt at a Solution

Should I set this up as to different functions such as Lim x-> 0 f(x) = +∞ and Lim x->0 g(x) = +∞
Is that way off?

I'm having a hard time trying to implement the 2 equations.
In either equation do I need to get a 0 in the denominator as 0+ which goes to +∞?
This question is tricky for me

 

[Dick]

Homework Statement

The ideal gas law from chem is PV = nRT. A process carried out at const. pressure is said to be isobaric. A process carried out at const. temperature is said to be isothermal.

A.) Using limits and the ideal gas law and assuming const. number of moles, show that that the volume of gas in an isobaric process goes to 0 as temperature goes to 0 and that the volume of gas in an isobaric process goes to +∞ as temperature goes to +∞. (Note: this is related to Charles' Law)

Homework Equations

PV=nRT
Charles Law: V1/T1 = V2/T2 or V2/V1 = T2/T1 or V1T2 = V2T1

The Attempt at a Solution

Should I set this up as to different functions such as Lim x-> 0 f(x) = +∞ and Lim x->0 g(x) = +∞
Is that way off?

I'm having a hard time trying to implement the 2 equations.
In either equation do I need to get a 0 in the denominator as 0+ which goes to +∞?
This question is tricky for me

V=nRT/P. P (pressure) is constant since it's isobaric, n (moles) is constant since the number of moles is constant. R is always constant. V(T)=constant*T. It's just one function. Now let T->0 and and T->infinity. Where's the tricky part?

 

[Torshi]

V=nRT/P. P (pressure) is constant since it's isobaric, n (moles) is constant since the number of moles is constant. R is always constant. V(T)=constant*T. It's just one function. Now let T->0 and and T->infinity. Where's the tricky part?

Are you implying:

lim t-> 0 (VT = nT)
and
lim t->∞ (VT = nT)

 

[Dick]

Are you implying:

lim t-> 0 (VT = nT)
and
lim t->∞ (VT = nT)

I'm not sure what that means and I'm also not sure what that has to do with what I said.

 

[Torshi]

I'm not sure what that means and I'm also not sure what that has to do with what I said.

Sorry. It's getting late.

So, are you suggesting simply have V = nRT/P with one being 0 and ∞ ?

 

[Dick]

Sorry. It's getting late.

So, are you suggesting simply have V = nRT/P with one being 0 and ∞ ?

It must be getting late. Yes, V=(nR/P)T. (nR/P) is a positive constant. Think about the limits as T->0 and T->infinity.

 

[Torshi]

It must be getting late. Yes, V=(nR/P)T. (nR/P) is a positive constant. Think about the limits as T->0 and T->infinity.

Alrighty..

Hmm. I'll tell you what I see and I know it's probably way off. But, I need to get my view or approach better for these problems

What my head is telling me and all I see is that (nR/P) is a positive value and as T approach 0 the value for V is getting smaller. I don't know if this has to do with anything. And vice versa for +∞.

I guess with these problems, I'm facing problems in regards of comprehending what I need to do or where to start.

 

[Dick]

Alrighty..

Hmm. I'll tell you what I see and I know it's probably way off. But, I need to get my view or approach better for these problems

What my head is telling me and all I see is that (nR/P) is a positive value and as T approach 0 the value for V is getting smaller. I don't know if this has to do with anything. And vice versa for +∞.

I guess with these problems, I'm facing problems in regards of comprehending what I need to do or where to start.

I don't think you are dealing with a 'proof' class where have to show anything. Just say what you think. How small can V get as T->0? How large can V get as T->infinity?

 

[Torshi]

I don't think you are dealing with a 'proof' class where have to show anything. Just say what you think. How small can V get as T->0? How large can V get as T->infinity?

-∞ with lim t->0 and +∞ with t->+∞

 

[Dick]

-∞ with lim t->0 and +∞ with t->+∞

You can't really think V is near -infinity if t is near 0, can you?

 

[Torshi]

You can't really think V is near -infinity if t is near 0, can you?

0 with lim t->0 and +∞ with t->+∞ in regards to V

V = (nR/P)T
V= (nR/P) * 0 = V near zero
-------------------------
V-(nR/P)T
V=(nR/P)*+∞ = V near +∞

 

[Torshi]

Also, if doing the same type of problem but relating the ideal gas law with boyles law P1V1=P2V2 can we show that the volume of gas in an isothermal process goes to +∞ as pressure goes to zero and that the volume of gas is an isothermal process goes to 0 as pressure goes to +∞.
T is constant= constant
Moles = constant
R = constantSo, V= (nR/P)T

Lim P->0 V = (nR/0)T --> V goes to +∞
and
Lim P->+∞ V = (nR/+∞)T --> V goes to 0

 

[Dick]

Also, if doing the same type of problem but relating the ideal gas law with boyles law P1V1=P2V2 can we show that the volume of gas in an isothermal process goes to +∞ as pressure goes to zero and that the volume of gas is an isothermal process goes to 0 as pressure goes to +∞.
T is constant= constant
Moles = constant
R = constant


So, V= (nR/P)T

Lim P->0 V = (nR/0)T --> V goes to +∞
and
Lim P->+∞ V = (nR/+∞)T --> V goes to 0

That sounds better.

 

[Torshi]

That sounds better.

Alright cool, thanks.