Question

An ideal Diesel Cycle has a compression ratio of 18 and a cutoff ratio of 1.5. Determine the maximum air temperature and the rate of heat addition to this cycle when it produces 200 hp of power; the cycle is repeated 1200 times per minute; and the state of the air at the beginning of the compression is 95 kPa and 17oC. Use constant specific heats at room temperature.

Answer 1

A) Q'_in = 304.66 hp

B) T_max = 1109.29 °C

Step-by-step explanation:

We are given;

compression ratio; r = 18

cutoff ratio; r_c = 1.5

Power; W' = 200 hp

Temperature; T1 = 17°C = 290 K

A) To find the rate of heat addition, we will use the derived formula;

Q'_in = (W' × r^(k - 1) × k(r_c - 1))/(r^(k - 1) × k(r_c - 1)) - ((r_c)^(k) - 1)

Where k is a constant = 1.4

Thus;

Q'_in = (200 × 18^(1.4 - 1) × 1.4(1.5 - 1))/((18^(1.4 - 1) × 1.4(1.5 - 1)) - ((1.5^(1.4)) - 1)

Q'_in = 304.66 hp

B) To find the maximum temperature, we will use the Formula;

T_max = T1 × r^(k - 1) × r_c

T_max = 290 × 18^(1.4 - 1) × 1.5

T_max = 1382.29 K

Converting to °C gives;

T_max = 1109.29 °C