# Thermodynamics Ideal gas problem

• Ron Burgundypants
In summary, the problem involves an isolated box with two chambers containing dilute gas at different densities and temperatures. The goal is to find the equilibrium temperature when the partition between the chambers is removed. By using the ideal gas law and considering the exchange of particles between the chambers, it is possible to solve for the equilibrium temperature without knowing the molar mass of the gas. The internal energy of an ideal gas mixture is related to the internal energy of the pure gases comprising the mixture, and by summing up the internal energies of both chambers, the equilibrium temperature can be determined.
Ron Burgundypants

## Homework Statement

An isolated box contains two chambers separated by a thermally insulating but moveable partition. Both chambers contain dilute gas (same kind) at different densities and temperatures. The left chamber contains 1.0 x 10^22 particles at 25 degrees celsius and the right chamber 6.0 x 10 ^21 particles at 15 degrees celsius. What is the equilibrium temp when the wall is removed?

## Homework Equations

PV=NkT
[Left Chamber] (mCv(Tf-Ti)) + [Right chamber](mCv(Tf-Ti))
Maybe the density equation?

## The Attempt at a Solution

What I understand;
- The volume is constant
- Chamber left loses some energy this is the same as what chamber right gains
- The Heat capacity is the same as the gas is the same in both chambers so we can forget it.

So I've tried all sorts of things but the problem is I don't know get how the number of particles can be exchanged for a mass seeing as we don't know which type of gas it is, otherwise the problem would be easy right? Just solve for Tf. Should I just use a random gas and get the molar mass etc. or is there a better way?

As you said, the gas is the same in both chambers, so you don't need to know the molar mass. You are aware that the gases mix after the partition is removed, correct? Do you know how the internal energy of an ideal gas mixture is related to the internal energy of the pure gases comprising the mixture?

Ron Burgundypants
The internal energy of an ideal gas is the degrees of freedom x NkT right? Not sure how to relate it to the total internal energy though no...

just write it out with letters and you will see it all cancels out
Ron Burgundypants said:
- Chamber left loses some energy this is the same as what chamber right gains

Ron Burgundypants
Ok I tried something and got an interesting answer. Might be right

Sum up the internal energies of both chambers i.e 3/2NRT(left) + 3/2 * NRT(right)

So this is the total internal energy - 3/2 NRT (total) - Solve for T now and I have the equilibrium temperature? Looks about right.

Wrongman I'll try your way too and see what happens if its easier. Thanks guys!

Aha! Yes brilliant thanks guys.

## 1. What is the ideal gas law in thermodynamics?

The ideal gas law is a fundamental equation in thermodynamics that describes the relationship between the pressure, volume, temperature, and amount of gas in a system. It is written as 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 temperature.

## 2. How do you solve ideal gas problems?

To solve ideal gas problems, you need to know the values of at least three of the variables in the ideal gas law (pressure, volume, temperature, and amount of gas). You can then rearrange the equation to solve for the unknown variable. It is important to convert all units to the appropriate SI units (Pascal, cubic meters, Kelvin, and moles) before plugging them into the equation.

## 3. What is the difference between an ideal gas and a real gas?

An ideal gas is a theoretical gas that follows the ideal gas law perfectly under all conditions. Real gases, on the other hand, deviate from the ideal gas law at high pressures or low temperatures. This is due to intermolecular forces and the finite size of gas molecules, which are not accounted for in the ideal gas law.

## 4. Can ideal gases exist in real life?

No, ideal gases do not exist in real life. All gases have some degree of deviation from the ideal gas law, although some gases may be closer to ideal behavior than others. At low pressures and high temperatures, most gases behave very closely to the predictions of the ideal gas law.

## 5. How is the ideal gas law used in practical applications?

The ideal gas law is used in various practical applications, such as in the design of internal combustion engines, refrigeration systems, and gas storage tanks. It is also used in the manufacturing of industrial gases, such as oxygen and nitrogen, and in the study of atmospheric gases in meteorology and climatology.

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