A rigid container has 1 kg argon at 300 K and kg argon at 400 K both at 150 kPa . Now they are a

A rigid container has 1 kg argon at 300 K and kg argon at...

A rigid container has 1 kg argon at $300 \mathrm{K}$ and $\mathrm{kg}$ argon at $400 \mathrm{K}$ both at $150 \mathrm{kPa} .$ Now they are allowed to mix without any external heat transfer. What is final $T, P ?$ Is any $s$ generated?

Key Concepts

Irreversible Process and Entropy Generation

Mixing gases that are initially at different temperatures in an isolated system is inherently irreversible, leading to the production of entropy. This entropy generation reflects the increase in disorder as the system moves from a non-equilibrium to an equilibrium state, making it an important aspect of the thermodynamic analysis.

Ideal Gas Model

Considering argon as an ideal gas means that its internal energy is solely a function of temperature and independent of pressure and volume. This assumption simplifies the analysis because it allows the use of straightforward energy equations without needing to account for interactions between particles.

Energy Conservation

In an adiabatic mixing process within a rigid container, the total internal energy of the system remains constant because there is no heat flow or boundary work. This principle allows the final state, particularly the final temperature, to be determined by balancing the initial internal energies of the different parts of the system.

Adiabatic Process

An adiabatic process is one in which there is no heat transfer into or out of the system. Since the system is insulated from thermal interactions with the surroundings, any changes in the system are due to internal energy redistribution alone, making energy conservation key.

Rigid Container

In thermodynamics, a rigid container is one that maintains a constant volume throughout the process, meaning no work is done by expansion or compression. This simplification focuses analysis on energy changes due solely to internal transformations rather than volume-related work.

Transcript

00:01 Hi, everybody.

00:01 So for this one is a rigid container has one kilogram of argon at 300k.

00:08 Now they are allowed to mix without any external heat transfer.

00:11 What is the final tp? okay.

00:16 So for this, we have your pressure 1a is going to equal to 150k pascal's.

00:30 And our energy zero, okay, for energy equation.

00:35 So we have u2 minus u1 for the energy, which equals going to equal zero.

00:40 And what we can do is take the mass of the both energies here and set it equal to zero.

00:48 Okay.

00:49 And what we're going to keep doing is do a 2m, cv, t2, which is the temperature, minus the cv of temperature.

01:00 Temperature 1a minus m, c, b of a temperature 1b, which equals 0.

01:08 And what we can do is take out the temperature and obviously knock out the m's here.

01:17 And we get t2 is going to equal to t1a plus t1b, which is divided by 2.

01:25 And if we look at we have argon mass equals one kilogram and the temperature of 1a equals 300 k okay oops and we're just going to put this into a box here and this argon over here is the same mass okay 1k, me 1 kilogram, and the temperature of 1b is actually 400 on this side.

02:02 So for this total temperature or 2t, t2, is going to be 300 plus 400 divided by 2, which is going to equal to 350k...

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