ME3321

Homework Set #10

Due: November 14, 2000

1. At the beginning of the compression process of an air-standard

Otto cycle, p1 = 1 bar, T1 = 290K, V1 = 400 cm^3. The maximum

temperature in the cycle is 2200K, and the compression ratio is 8.

Determine:

(a) the heat addition in kJ

(b) the net work in kJ

(d) the mean effective pressute in bars (mep is defined in equation 9.1)

(e) DON'T DO THIS PART.

We will treat air as an ideal gas (pv = RT). Also, Table A-22 is available

for our use. In addition, please make use of the p-v and T-s diagrams that

are displayed in the solution of example problem 9-1.

The most effective approach to the solution is to obtain the properties at

each state. For state 1, use the given temperature and look up u1 and

vr1 in Table A-22.

To find state 2, please note that the process 1 -> 2 is isentropic (see

diagrams for example problem 9-1). Also, the compression ratio V1/V2 =

v1/v2 = 8. Also, for an isentropic process such as 1 -> 2, the specific

volumes at the end states 1 and 2 are related by

v2/v1 = vr2/vr1

where the values of vr are listed in Table A-22. In our problem, with

v2/v1 = 1/8 and vr1 = 676.1, we solve for vr2 and get vr2 = 84.5125.

With this value of vr2, Table A-22 gives T2 = 652.4 and u2 = 475.11

kJ/kg.

The maximum temperature of the cycle is given as 2200K, so that T3 = 2200K.

This information allows us to find u3 and vr3 from Table A-22.

Since 3 and 4 are connected by an isentropic process,

v4/v3 = vr4/vr3

where v4/v3 = 8 and vr3 = 2.012. Therefore, vr4 can be found, and table

look up (A-22) gives T4 and u4.

The unknown mass m of the system is determined from state 1 since p, V, and

T are known at that state, and pV = mRT.

Please complete the problem.

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2. Problem 9.17 (page 442 of the 3rd edition and page 502 of the 4th

edition)

The air-standard Atkinson cycle described in the problem statement is

a slight variant of the Otto cycle. The problem statement asks that

the Atkinson cycle results be compared with those for the corresponding

Otto cycle which were obtained in problem 9.1. Here are the results

from problem 9.1: Wcycle = 721.12 kJ/kg, eta = 0.515, mep = 949.2 kPa.

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3. Problem 9.19 (page 443 of the 3rd edition and page 502 of the 4th

edition)

This problem is very similar to example problem 9.2. Please read the

solution of the example problem before solving problem 9.19. Along an

isentropic process between two states and 2,

v2/v1 = vr2/vr1 and p2/p1 = pr2/pr1

where values of vr and pr are listed in Table A-22.

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