Thermal Efficiency in an Ideal Diesel cycle.

[MacLaddy]

Homework Statement

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%

Homework Equations

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

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

 

[Andrew Mason]

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

 

[MacLaddy]

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

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