Thermodynamics - reversible isothermal cycle

In summary, the individual is asking for help with a homework problem involving a gas going from state A to B. They have attempted to solve it by using the ideal gas law and integrating the pressure-volume equation, but their final answer is incorrect. After receiving guidance from another person, they realize their mistake and are able to correct their calculation to get the correct answer of -8.15 kJ.
  • #1
Feodalherren
605
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
 
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  • #2
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
 
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Likes 1 person
  • #3
Hmm...

50 / (.0820582) = 609 K

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

Related to Thermodynamics - reversible isothermal cycle

What is a reversible isothermal cycle?

A reversible isothermal cycle is a thermodynamic process in which the temperature remains constant throughout the entire cycle. This means that the system is in thermal equilibrium with its surroundings at all times.

What is the purpose of a reversible isothermal cycle?

The purpose of a reversible isothermal cycle is to convert heat energy into work, or vice versa. This is achieved by following a specific path on a pressure-volume diagram, known as the Carnot cycle.

How is a reversible isothermal cycle different from other cycles?

A reversible isothermal cycle is different from other cycles because it maintains a constant temperature throughout the entire process. This is in contrast to other cycles, such as adiabatic or isobaric cycles, where the temperature can change.

What are the limitations of a reversible isothermal cycle?

One limitation of a reversible isothermal cycle is that it can only occur in a system with perfect thermal insulation. This means that there is no heat exchange with the surroundings during the process. Another limitation is that it can only occur in an ideal, frictionless system.

How is the efficiency of a reversible isothermal cycle calculated?

The efficiency of a reversible isothermal cycle is calculated using the formula: efficiency = 1 - (Tcold/Thot). Tcold and Thot represent the temperatures at which heat is absorbed and released, respectively, during the cycle.

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