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Item110pointseBook HintPrintReferences Check my work Check My Work button is now disabled5Item 1Item 1 10 pointsAn 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 150 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 17°C. Use constant specific heats at room temperature. The properties of air at room temperature are cp = 1.005 kJ/kg·K, cv = 0.718 kJ/kg·K, R = 0.287 kJ/kg·K, and k = 1.4.

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Answer:

The answer is given below

Explanation:

Given that:

Compression ratio (r) = 18, cut off ratio ([tex]r_c[/tex]) = 1.5, k = 1.4, W = 150 hp, initial temperature (Ti) = 17°C = 290 K

The rate of heat addition (Qin) is given by the equation:

[tex]Q_{in}=\frac{W*r^{k-1}*k(r_c-1)}{r^{k-1}*k(r_c-1)-(r_c^k-1)} \\\\substituting\ values\ into\ the \ equation\ gives:\\\\Q_{in}=\frac{150*18^{1.4-1}*1.4(1.5-1)}{18^{1.4-1}*1.4(1.5-1)-(1.5^{1.4}-1)}=\frac{333.6555}{2.2244-0.7641} =\frac{333.6555}{1.4603} =228.5\ hp[/tex]

Therefore, The rate of heat addition is 228.5 hp

The maximum air temperature is determined using the Compression ratio, cut off ratio and the initial temperature. The maximum air temperature ([tex]T_{max}[/tex]) is given by the formula:

[tex]T_{max}=T_{in}*r^{k-1}*r_c=290*18^{1.4-1}*1.5=1382.3\ K=1109.3^oC[/tex]

The maximum air temperature is 1109.3°C

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