# Thermal Efficiency in an Ideal Diesel cycle.

1. Nov 30, 2013

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.

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

Thanks,
Mac

2. Dec 1, 2013

### 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

3. Dec 1, 2013