Thermodynamics: Heat and Work

In summary, we had two chambers with different gas concentrations, adiabatic walls, and a diathermanous piston. We added heat until the pressure in the right chamber was 2 bars. The left chamber was a polytropic process with n=-2. The final temperature in the right chamber was 351.57 degrees Kelvin.
  • #1
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Homework Statement


-We have a cylinder with two chambers separated by an adiabatic piston. The external walls are adiabatics but left wall is diatermana. Friction produced by the piston moving is absorbed by the right system. Inicially gas conditions are the same for both ( in the left chamber CO2, 500 litres, 1 Bar, 27 ºC, and in right chamber N2 with the same conditions).
We add heat (by an exterior focus with constant temperature of 900ºK) through diatemana wall and piston moving until pressure in right chamber is 2 Bar. Left system is a polytropic process with n = -2. We assume gases are perfect.
Calculate:
a) P,T,V in final equilibrium in both chambers
b) ΔU , heat and work in left chamber
c) ΔU , heat and work in right chamber
d) Expansion work and friction work in right chamber

Homework Equations





The Attempt at a Solution


a) First I find moles for both gases and It`s the same 20.32 moles.
Final pressure in both chambers is 2 Bar. To calculate final temperature in left chamber I used [tex]T_2=T_1(P_2/P_1)^{n-1/n} [/tex]and it is [tex] T_2=848,52 ºK.[/tex]
For the volume [tex] P_1(V_1)^n=P_2(V_2)^n [/tex] and it is [tex]V_2= 707,1 Litres[/tex]
For the right chamber: Total volume of the cylinder is 1000 litres and doesn´t change, so [tex]V_t=V_{1f}-V_{2f}, 1000=707,1-V_{2f}, V_{2f}=292,9 litres[/tex] now I used [tex]PV=NRT[/tex] to calculate final temperature in right chamber [tex]T=351,57 ºK.[/tex]
b) To calculate ΔU, I use [tex]ΔU= N Cv(Tf-Ti)[/tex] and [tex] ΔU=229.0788 Kj [/tex] after
[tex]W_{exp}=NR(T_f-T_i)/1-n [/tex] and [tex]W_{exp}=30.8901 Kj [/tex] Now I calculate Q
[tex] Q= ΔU+W_{exp}=198.1887 Kj [/tex]

I don´t know if it´s ok?
Thank you
 
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  • #2
You have followed it through well.

The only thing that bothers me about this calculation is the value of 2 for n.
Where did this come from?

I have
For carbon dioxide n=1.2
For nitrogen n=1.4

Incidentally I apologise for confusing Italian with Spanish before.
The English word is diathermanous.

go well
 
  • #3
Hello Studiot,thank you for your reply.The n value is an exercise data,is given by the teacher,I suppose it`s invented. Thank you to correct diathermanous word.
Best regards
 
  • #4
Seems a bit pointless stating the gas, then supplying the wrong value of the ratio of specific heats.

Further, I presume you realize that the stated conditions are instantaneous?
With the heat source specified the gas in the left chamber would continue to heat up until its temperature was the same as the heat source.

I normally expect to see given information used (needed) in some way in a question. Does your teacher not do this?
 
  • #5
Hello, unfortunaly we have a very bad teacher for this subject.
Thank you
 

What is the definition of thermodynamics?

Thermodynamics is a branch of physics that deals with the relationship between heat, work, temperature, energy, and their effects on matter.

What is the first law of thermodynamics?

The first law of thermodynamics, also known as the Law of Conservation of Energy, states that energy cannot be created or destroyed, but can only be transferred or converted from one form to another.

What is the second law of thermodynamics?

The second law of thermodynamics states that in any energy conversion or transfer, the total entropy (disorder or randomness) of the system and its surroundings will always increase.

What is the difference between heat and work in thermodynamics?

Heat and work are both forms of energy, but they differ in how they are transferred. Heat is the transfer of energy due to a temperature difference, while work is the transfer of energy due to a force acting over a distance.

What are some real-life applications of thermodynamics?

Thermodynamics has many practical applications, including designing efficient engines, refrigeration systems, and power plants. It also plays a crucial role in understanding weather and climate patterns, as well as chemical reactions and processes in the human body.

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