Thermodynamics - reversible isothermal cycle

Click For Summary
SUMMARY

The discussion focuses on solving a problem related to a reversible isothermal cycle in thermodynamics. The user initially calculated the temperature (T) as 882 K using the ideal gas law PV=nRT, but later realized that the correct temperature should be 609 K after clarifying the units. The work done (w) was incorrectly calculated as -11.8 kJ instead of the expected -8.15 kJ. The correct calculation involves using the appropriate value of R and ensuring the temperature is in Kelvin.

PREREQUISITES
  • Understanding of the ideal gas law (PV=nRT)
  • Knowledge of thermodynamic cycles, specifically isothermal processes
  • Familiarity with integration in calculus, particularly for pressure-volume work
  • Ability to convert temperature units accurately
NEXT STEPS
  • Review the derivation of work done in isothermal processes in thermodynamics
  • Learn about the implications of using different values of the gas constant R in calculations
  • Study the concept of reversible processes and their significance in thermodynamics
  • Explore common mistakes in thermodynamic calculations and how to avoid them
USEFUL FOR

Students studying thermodynamics, educators teaching thermodynamic principles, and anyone involved in solving problems related to gas laws and thermodynamic cycles.

Feodalherren
Messages
604
Reaction score
6

Homework Statement



Untitled.png


Homework Equations


The Attempt at a Solution



I can do everything else except work for part one going from A to B.

What I did was

-∫PdV = -nRT ∫(1/v)dV = -nRT ln (Vf/Vi)

I can solve for T because everything is given, T in Kelvin is 882.
From PV=nRT
T=(5atm)(10L)/1mol*R = 882K

where R = .0820582

Therefore w= -1mol * R * 882 * ln (5) = - 11.8kJ

where R = 8.314

But this is incorrect. It is supposed to be -8.15kJ
 
Physics news on Phys.org
Feodalherren said:


The Attempt at a Solution



I can do everything else except work for part one going from A to B.

What I did was

-∫PdV = -nRT ∫(1/v)dV = -nRT ln (Vf/Vi)

I can solve for T because everything is given, T in Kelvin is 882.
From PV=nRT
T=(5atm)(10L)/(1mol*R) = 882K

where R = .0820582



Redo the calculation in red.

ehild
 
  • Like
Likes   Reactions: 1 person
Hmm...

50 / (.0820582) = 609 K

Argh nevermind I thought it gave me the T in celsius! Thank you Ehild!
 

Similar threads

  • · Replies 1 ·
Replies
1
Views
1K
Replies
4
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 5 ·
Replies
5
Views
8K