# Using Ideal Gas Law and Charles Law to compute limit

• Torshi
In summary, using the ideal gas law and assuming constant number of moles, it can be shown that in an isobaric process, the volume of gas goes to 0 as temperature goes to 0 and goes to +∞ as temperature goes to +∞, which is related to Charles' Law. Similarly, in an isothermal process, the volume of gas goes to +∞ as pressure goes to 0 and goes to 0 as pressure goes to +∞, which is related to Boyle's Law.
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

Torshi said:

## 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?

Dick said:
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)

Torshi said:
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.

Dick said:
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 ∞ ?

Torshi said:
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.

Dick said:
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.

Torshi said:
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?

Dick said:
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->+∞

Torshi said:
-∞ with lim t->0 and +∞ with t->+∞

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

Dick said:
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 +∞

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

Torshi said:
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.

Dick said:
That sounds better.

Alright cool, thanks.

## 1. What is the Ideal Gas Law and how is it used to compute limits?

The Ideal Gas Law is a fundamental equation in thermodynamics that describes the relationship between the pressure, volume, and temperature of an ideal gas. It is represented by the formula PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the gas constant, and T is the temperature. By rearranging this formula, we can use it to compute limits by substituting different values for pressure, volume, and temperature.

## 2. How does Charles Law relate to the Ideal Gas Law?

Charles Law is a specific case of the Ideal Gas Law that states that at a constant pressure, the volume of an ideal gas is directly proportional to its temperature. This can be expressed as V1/T1 = V2/T2, where V1 and T1 are the initial volume and temperature, and V2 and T2 are the final volume and temperature. This relationship is essential in calculating the limit of an ideal gas using the Ideal Gas Law.

## 3. Can the Ideal Gas Law be used for all types of gases?

The Ideal Gas Law is a theoretical equation that only applies to ideal gases, which have no intermolecular forces. However, it can be used as an approximation for real gases at low pressures and high temperatures. For more accurate calculations, other gas laws, such as the van der Waals equation, should be used.

## 4. How can the Ideal Gas Law be used to find the limit of a gas at a specific temperature and pressure?

To compute the limit of an ideal gas at a given temperature and pressure, we can use the Ideal Gas Law to solve for the volume. We can then substitute this volume into the Charles Law equation to find the volume of the gas at a different temperature or pressure. By repeating this process with different values, we can determine the limit of the gas.

## 5. What are the units used in the Ideal Gas Law and how should they be converted?

The units used in the Ideal Gas Law depend on the values being calculated. Pressure is typically measured in atmospheres (atm), volume in liters (L), temperature in Kelvin (K), and the number of moles in moles (mol). If different units are used, they should be converted to these units before applying the Ideal Gas Law equation.

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