Work and Ideal Gases: Calculate Initial Volume

In summary: GEEEEE! Thanks so much for your help, everyone!In summary, Homework Statement mole of ideal gas does 1975 J of work on the surroundings as it expands isothermally to a final pressure of 1.2 atm and a volume of 24 L. find the initial volume.
  • #1
Jake4
111
1

Homework Statement



One mole of an ideal gas does 1975 J of work on the surroundings as it expands isothermally to a final pressure of 1.2 atm and a volume of 24 L.

find the initial volume. The universal gas constant is 8.31451 J/K mol




The Attempt at a Solution



Something he touched on in class, but I don't have relevant equations in my notes.

thanks guys!
 
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  • #3
It seems as if for the work equations, I would also need the Temperature. Is there a way around that? or possibly an equation that allows me to get it?

Also, this is one of those things, that I just simply haven't done before... but how would I solve for a variable within the ln?

you end up with W=nRT*lnVf/Vi So how would I be solving for that Vi?
 
  • #4
Jake4 said:
It seems as if for the work equations, I would also need the Temperature. Is there a way around that? or possibly an equation that allows me to get it?

Also, this is one of those things, that I just simply haven't done before... but how would I solve for a variable within the ln?

you end up with W=nRT*lnVf/Vi So how would I be solving for that Vi?


Let's take this one step at a time.
That is, let's first set up the equations.
After that we'll see how we can solve them. :smile:


You ask how you can get the temperature T.
Well, perhaps you have overlooked the relevant equation on the wiki page.

It's:

p V = n R T​



Can you set up the equations? :confused:
 
  • #5
Jake4 said:
It seems as if for the work equations, I would also need the Temperature. Is there a way around that? or possibly an equation that allows me to get it?
T = PV/nR

Also, this is one of those things, that I just simply haven't done before... but how would I solve for a variable within the ln?

you end up with W=nRT*lnVf/Vi So how would I be solving for that Vi?
Use:

[tex]e^{\ln x} = x[/tex]AM
 

1. What is the ideal gas law and how is it used to calculate initial volume?

The ideal gas law, also known as the universal gas law, is a mathematical equation that describes the relationship between the pressure, volume, temperature, and number of moles of a gas. It is often used to calculate the initial volume of a gas when the other variables are known. The equation is expressed as PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin.

2. How does the number of moles affect the initial volume of a gas?

The number of moles of a gas is directly proportional to the initial volume of the gas. This means that as the number of moles increases, the initial volume of the gas also increases, and vice versa. This relationship is described by the ideal gas law, where n is one of the variables.

3. Can the ideal gas law be used for all gases?

No, the ideal gas law is only applicable to ideal gases which follow certain assumptions, such as having negligible molecular size and no intermolecular forces. Real gases, on the other hand, deviate from these assumptions and may require different equations or corrections to accurately calculate their initial volume.

4. How does temperature affect the initial volume of a gas?

According to the ideal gas law, the initial volume of a gas is directly proportional to its temperature in Kelvin. This means that as the temperature increases, the initial volume of the gas also increases, and vice versa. This relationship is also known as Charles's Law.

5. What units should be used for each variable in the ideal gas law equation?

The units for pressure (P) should be in Pascal (Pa), volume (V) in cubic meters (m3), temperature (T) in Kelvin (K), and the gas constant (R) in Joules per mole-Kelvin (J/mol-K). It is important to ensure that all units are consistent to obtain accurate results.

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