1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Thermal Efficiency in an Ideal Diesel cycle.

  1. Nov 30, 2013 #1

    MacLaddy

    User Avatar
    Gold Member

    1. The problem statement, all variables and given/known data

    Helium in an ideal Diesel cycle is compressed from 4 L to 0.25 L, and then it expands during the constant pressure heat addition process to 0.50 L. Under air standard conditions, the thermal efficiency of this cycle is:

    a) 79.5%
    b) 20.5%
    c) 61.4%
    d) 67.4%
    e) 84.3%

    2. Relevant equations

    $$\eta_{TH}=1-\frac{1}{r^{k-1}}[\frac{r_c^k-1}{k(r_c-1)}]$$
    $$r_c = \frac{v_3}{v_2}=\frac{0.50L}{0.25L}=2$$
    $$r=\frac{v_1}{v_2}=\frac{4}{0.25}=16$$

    3. The attempt at a solution

    My main problem with this question is in the wording. "Under air standard conditions" I typically would use the k value of 1.4, but as it specifically states "Helium" I wonder if I shouldn't use k=1.667.

    k=1.667 my answer is 79.5%
    k=1.4 my answer is 61.4%

    Any help on what the standard operation with this type of wording is would be greatly appreciated.

    Thanks,
    Mac
     
  2. jcsd
  3. Dec 1, 2013 #2

    Andrew Mason

    User Avatar
    Science Advisor
    Homework Helper

    I am not sure how helium works in a Diesel engine. But you aren't supposed to worry about that.

    I suggest that you just assume that the system consists of only He connnected to hot and cold reservoirs. The cycle is comprised of a constant pressure expansion while connected to the hot reservoir, then an adiabatic expansion, then a constant volume cooling when connected to the cold reservoir, followed by adiabatic compression. Use the efficiency formula for the Diesel using the gamma for He.

    AM
     
  4. Dec 1, 2013 #3

    MacLaddy

    User Avatar
    Gold Member

    Thank you, the gamma was based on Helium. Now I'm going to go build a Diesel Engine that runs on helium... (who writes this stuff?)

    Mac
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted