Subtopic: Thermodynamic principles of I.C. engines
Question Statement:
Which of the following statements regarding the air-standard thermodynamic cycles of Internal Combustion (I.C.) engines are TRUE?
Options:
(A) For the same compression ratio and heat addition, the air-standard thermal efficiency follows: $\eta_{Otto} > \eta_{Dual} > \eta_{Diesel}$
(B) For the same maximum peak pressure and maximum temperature, the air-standard efficiency follows: $\eta_{Diesel} > \eta_{Dual} > \eta_{Otto}$
(C) In an air-standard Diesel cycle, increasing the cut-off ratio while keeping the compression ratio constant increases the thermal efficiency
(D) The thermal efficiency of an air-standard Otto cycle depends solely on the compression ratio and the adiabatic index $\gamma$
Answer Key:
A, B, D
Step-by-Step Solution & Explanation
1. For the same compression ratio $r$ and heat input, heat rejection in Diesel is greater than in Otto, so $\eta_{Otto} > \eta_{Dual} > \eta_{Diesel}$. (Statement A is True)
2. For the same peak cylinder pressure and temperature, Diesel cycle accepts more heat at constant pressure, giving $\eta_{Diesel} > \eta_{Dual} > \eta_{Otto}$. (Statement B is True)
3. In a Diesel cycle, efficiency is $\eta = 1 - \frac{1}{r^{\gamma - 1}} \left[\frac{r_c^\gamma - 1}{\gamma(r_c - 1)}\right]$. As cut-off ratio $r_c$ increases, the term in bracket increases, which REDUCES thermal efficiency. (Statement C is False)
4. Otto efficiency is $\eta = 1 - \frac{1}{r^{\gamma - 1}}$, governed solely by $r$ and $\gamma$. (Statement D is True)