Calculate these 5 temperatures along this Thermodynamic cycle

  • #1
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Homework Statement
Calculate the temperatures at places 2, 4, A, B and C if you know:
It's an ideal diatomic gas
T3 = 4T1
T2 = Tb = T4
The axis connecting 1, B and 3 crosses zero.
Relevant Equations
pV = nRT
Laws of thermodynamics
Screenshot_20230325_165532_WPS Office.jpg

I only know T3 = 4•T1
I was able to calculate the T2 = Tb = T4
I built four equations:
T2 = p2V1 / nR
T4 = p1V2 / nR
p1/T1 = p2/T2
V1/T2 = V2/4T1

I put them together and got T2 = 2T1

I can't figure out the temperatures of A and C. I tend to think Ta could equal Tc (then I would be able to calculate it), but I am not sure.
 
Last edited:

Answers and Replies

  • #2
Helo @Seeit ,
:welcome: ##\qquad## !​
Are you sure you have rendered the complete problem statement ? I would expect some more information, like: ideal gas, isothermal (or adiabatic), ...

I also miss an equation of state in your relevant equations (e.g. ##\ pV = NRT##).

I only know ##T_3 = 4T_1##
How ? Or was that a given ? (In that case it is part of the problem statement)
Same for ##T_2 = T_b = T_4## ?

What about the scale and the axes of the diagram ?

##\ ##
 
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Likes Seeit and Lnewqban
  • #3
Welcome, @Seeit !

As post #1 has been edited to answer @BvU questions, I suggest considering two things:

-The inverse proportionality between p and V.
-The similarity between polygons 1CBA and 1234 due to the axis connecting 1, B and 3, which makes their corresponding sides proportional.

direct-and-inverse-proportion-1629696427.png
 
  • Like
Likes Seeit and BvU
  • #4
Welcome, @Seeit !

As post #1 has been edited to answer @BvU questions, I suggest considering two things:

-The inverse proportionality between p and V.
-The similarity between polygons 1CBA and 1234 due to the axis connecting 1, B and 3, which makes their corresponding sides proportional.

View attachment 324057
So am I right about thinking that A and C are on the same isotherm and have therefore the same temperature?
 
  • #5
So am I right about thinking that A and C are on the same isotherm and have therefore the same temperature?
Correct!
 

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