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How to show that Carnot engine is more efficient?

  1. Dec 12, 2016 #1
    1. The problem statement, all variables and given/known data
    Consider an Ideal gas engine with the following cycle:
    i. Isobaric expansion (T1 -> Th)
    ii. adiabatic expansion (Th -> T2)
    iii. Isobaric compression (T2 -> T_L)
    iv. adiabatic compression (T_L -> T1)
    a. Find its efficiency
    b. When operated in two temperature, show that Carnot engine is more efficient

    2. Relevant equations

    Efficiency of the Ideal gas engine: $$e=1-\frac{T_2 - T_L}{T_H - T_1}$$

    Efficiency of the Carnot Engine: $$e=1-\frac{T_L}{T_H}$$

    3. The attempt at a solution

    I try to approximate the efficiency of the Ideal gas when T1 is very close to TH and TL is very close to T2, T1~TH, TL~T2, then subtract it to the Carnot Efficiency, if it turns out to become positive then Carnot Engine is more efficient. However I get an Indefinite for the Ideal gas efficiency since the denominator becomes zero.
     
  2. jcsd
  3. Dec 12, 2016 #2

    TSny

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    Homework Helper
    Gold Member

    Useful information: two legs of the cycle for the ideal gas are adiabatic processes between the same pressures.
     
    Last edited: Dec 12, 2016
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