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Beer-monster
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Homework Statement
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?
Homework Equations
Ideal gas law: [tex]PV = Nk_{B}T = nRT [/tex]
Where n= N/Na
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
[tex] P^{1-\gamma}T^{\gamma} = constant [/tex]
Where for a monatomic ideal gas (such as Argon) [tex]\gamma=\frac{5}{3}[/tex]
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