Class Exercise 1 - Otto

 

  Class Exercise: Otto Cycle

1.

The compression ratio of an air-standard Otto cycle is 9.0. Prior to the isentropic compression process, the air is at 100 kPa, 300 K and 500 cm 3. The temperature at the end of the isentropic expansion process is 800 K. Assume constant specific heat during the processes. a.

Sketch the  p–v and T-s diagrams of the cycle.

b.

Determine:

c.

i.

the highest temperature and pressure in the cycle,

ii.

the amount of heat input in kJ, and

iii.

the thermal efficiency of the cycle.

Discuss the effect of increasing the compression ratio on the thermal efficiency of the cycle. [T2=722.47K, T3=1926.58K =1926.58K,, P2=2167.4 kPa, P3=5779.7 kPa; Q23=0.502 kJ; 58.47%]

2.

An air-standard Otto cycle has a compression ratio of 7.5. At the beginning beginning of compression, compression, air is at 32oC and 85 kPa. The mass of air is 2 grams, and the maximum temperature in the cycle is 687 oC. Account for variation of specific heats with temperature. a. b.

Sketch the  p–v diagram and label the processes. Determine the temperature and the internal energy at all the states of the cycle.

c.

Calculate the amount of heat rejected from the cycle and the amount of heat added to the cycle.

d.

Determine the net work output and the thermal efficiency.

e.

Determine the mean effective pressure. [T2=667.4K, u2=486.77 kJ/kg, T4=458.7K, u4=329.01 kJ/kg; Q41=0.2227 kJ,Q23= 0.4765 kJ; Wnet=0.2538 kJ, 53.3%; MEP=142.2 kPa]

3.

At the beginning beginning of compression compression of an air-standard Otto cycle, the inlet pressure, P 1 = 1 bar, temperature, T 1 = 290K, and volume, V 1 = 400 cm3. The maximum temperature in the cycle is 2200K and the compression ratio is 8. Assume the inlet air condition to be T 0 0 = 290 K, and   P 0  1 bar. bar. Determine for the cycle: cycle: 0 =  

a.

The heat addition, Qin in kJ.

b. c.

The net work, W nnet  et  in kJ. The thermal efficiency,  th .

d.

The mean effective pressure, in bar.

e.

The exergy transferred to the air during the heat addition, in kJ.

f.

The exergy efficiency for the cycle.

[T2=652.4K, T4=1159.3K, Q23=0.6715 kJ, W net=0.3397 kJ, 50.6%, MEP=9.71 bar, EQ=0.522 kJ, EW=0.3397 kJ]