How Do You Calculate Thermal Efficiency in a Diatomic Gas Heat Engine Cycle?

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SUMMARY

The discussion focuses on calculating the thermal efficiency of a heat engine utilizing 1.00 mol of an ideal diatomic gas through a specified cycle. The thermal efficiency (e) is defined by the equation e = W/Q_{H} = 1 - |Q_{C}/Q_{H}|, where W represents work done and Q_{H} is the heat input. The user successfully identified that the heat entering the system during the isobaric segment (bc) can be calculated using the specific heat capacity at constant pressure (C_p). The problem's complexity arises from the need to differentiate between various thermodynamic cycles, specifically noting that the Carnot cycle is not applicable in this scenario.

PREREQUISITES
  • Understanding of thermodynamic cycles, specifically isobaric and isochoric processes.
  • Knowledge of the ideal gas law and properties of diatomic gases.
  • Familiarity with the concepts of heat transfer and work in thermodynamic systems.
  • Ability to apply specific heat capacities (C_p and C_v) in calculations.
NEXT STEPS
  • Study the derivation and application of the first law of thermodynamics in heat engines.
  • Learn how to calculate work done in isobaric and isochoric processes for ideal gases.
  • Explore the differences between Carnot, Otto, and other thermodynamic cycles.
  • Investigate the specific heat capacities of diatomic gases and their implications in thermal efficiency calculations.
USEFUL FOR

This discussion is beneficial for students in thermodynamics, mechanical engineers designing heat engines, and anyone interested in the principles of energy conversion in diatomic gas systems.

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Homework Statement



You build a heat engine that takes 1.00 mol of an ideal diatomic gas through the cycle abc, where segment bc is isobaric and segment ca is isochoric. calculate the thermal efficiency of the engine.

this is a 5 part problem and I already solved for Wo and Wo=Qo I solved for Ta, Tb, and Tc. Ta=Tb. the problem gives me Va, Vb, Pa, and Pb in the figure.

Homework Equations



e = W/Q_{H} = 1 - |Q_{C}/Q_{H}|

W = |Q_{H}| - |Q_{C}|

The Attempt at a Solution



I know that there are other ways to solve for e, but I don't know how to solve for e in this problem. I am completely lost. I can't use Carnot because that's for an ideal system, I can't use the one for the otto cycle because i don't have r and the problem doesn't tell me that it is otto cycle problem. WHAT DO I DO?
 
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also the segment ab is isothermic. I don't see how that would help any though
 
just kidding, i just figured it out. i can use the equation of heat entering the system which is Qh which is on segment bc which is isobaric so i can use Cp to solve for Qh!
 

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