# Thermodynamics: Ideal gas splitting invention problem

1. Aug 27, 2011

### Beer-monster

1. The problem statement, all variables and given/known data

4. An inventor would like to patent a thermodynamic device and is making
the following claims:

The device can accept a stream of gas and split it into a hot and cold jet of
the same gas. This device is said to contain no moving parts, consumables, or
power supply and it is claimed to operate in different modes such that it can:

A. accept an ideal gas (e.g. argon) at 4 atm, 20 ◦ C, 2 mol/min and output
one stream of 1 mol/min at 1atm, T=-20 ◦ C and, simultaneously, a second
stream at 1 mol/min, 1atm, T=60 ◦ C

B. accept an ideal gas at 4 atm, 20 ◦ C, 2 mol/min and output one stream
of 1.5 mol/min at 1atm, T=0 ◦ C and, simultaneously, a second stream at
0.5 mol/min, 1atm, T=90 ◦ C

C. accept an ideal gas at 1.1 atm, 20 ◦ C, 2 mol/min and output one stream
of 1.6 mol/min at 1atm, T=-30 ◦ C and, simultaneously, a second stream
at 0.4 mol/min, 1atm, T=220 ◦ C

Which of these claims would you reject? Which ones would you accept and
why?

2. Relevant equations

Ideal gas law: $$PV = Nk_{B}T = nRT$$

Where n= N/Na

3. The attempt at a solution

My first thought was to try and think of a quantity that should remain constant through the process, so that I could calculate it for the initial conditions and for the products and compare.

As the question says there is no power source, fuel etc I would assume that there is no external heat being input into the system and thus it's an adiabatic process. So I tried calculating

$$P^{1-\gamma}T^{\gamma} = constant$$

Where for a monatomic ideal gas (such as Argon) $$\gamma=\frac{5}{3}$$

However, this plan didn't work out. The values were difficult for A,B and C and I'm sure at least one of the options should be accurate.

Can anyone tell me the flaw in my logic and perhaps point me in the right direction.

Thanks
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Aug 27, 2011

### ninco

I would say A and B are impossible.
For example, A takes as input 4 atm pressure at 20C and outputs the same mass of gas with the pressure reduced to 1 atm. That requires a big drop in temperature.
But the output temperatures claimed average to 20C (the same as the input).

B isn't very different.

C on the other hand looks to be just possible - the average temperature of the output is not far off 20C and the pressure is only slightly different - but you would need to check the calculation accurately, I'm just estimating.

3. Aug 27, 2011

### Beer-monster

When you say calculation, do you mean the relationship between P and T I quotedor adiabtic processes, or something else.

I found it hard to really judge the relationship between T and P without knowing anything about the volume changes.