Question Bank • QB_FP_027 NAT • 2 Marks

Section 3: Farm Power

Farm Power

Subtopic: I.C. engine cycles

Question Statement:

An ideal Dual combustion (limited pressure) cycle has a compression ratio $r = 14.0$, pressure ratio during constant volume heat addition $\alpha = P_3/P_2 = 1.50$, and cut-off ratio during constant pressure heat addition $r_c = V_4/V_3 = 1.40$. With $\gamma = 1.40$, the bracketed cut-off factor $K = \frac{\alpha r_c^\gamma - 1}{(\alpha - 1) + \gamma \alpha (r_c - 1)}$ in the thermal efficiency formula is equal to ________ (round off to 2 decimal places).

Answer Key:

1.05

Step-by-Step Solution & Explanation

Calculate numerator and denominator: 1. Numerator: $\alpha r_c^\gamma - 1$ $r_c^\gamma = 1.4^{1.40} \approx 1.6020$ $\alpha r_c^\gamma = 1.50 \times 1.6020 = 2.4030$ $\text{Numerator} = 2.4030 - 1 = 1.4030$ 2. Denominator: $(\alpha - 1) + \gamma \alpha (r_c - 1)$ $(\alpha - 1) = 1.50 - 1 = 0.50$ $\gamma \alpha (r_c - 1) = 1.40 \times 1.50 \times (1.40 - 1) = 2.10 \times 0.40 = 0.84$ $\text{Denominator} = 0.50 + 0.84 = 1.34$ 3. Value of factor $K$: $K = \frac{1.4030}{1.34} \approx 1.047 \approx 1.05$
← Previous (QB_FP_028) Next (QB_SUBEXP_S3_001) →

Practice In Authentic CBT Exam Interface

Test your skills under authentic timed conditions with live scoring and AIR percentile ranking.

Launch CBT Mock Test