Solving Otto Cycle Problem: Find p2, p3, p4, T2, T3, T4, V2, V3, V4

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SUMMARY

The discussion focuses on solving the Otto Cycle problem, specifically finding the parameters p2, p3, p4, T2, T3, T4, V2, V3, and V4 given known values of p1, V1, T1, ε (compression ratio), R, and k. Key equations utilized include the relationships between volumes, temperatures, and pressures during the cycle, such as ε = V1 / V2 and the ideal gas law p * V = R * T. The user encountered difficulties in determining p3 and p4, concluding that additional information about either pressure or temperature at the upper points is necessary to fully solve the problem.

PREREQUISITES
  • Understanding of the Otto Cycle and its thermodynamic processes
  • Familiarity with the ideal gas law (p * V = R * T)
  • Knowledge of thermodynamic properties such as compression ratio (ε) and specific heat ratio (k)
  • Ability to manipulate equations involving temperature and volume relationships
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  • Study the derivation and application of the Otto Cycle equations
  • Learn about the implications of the ideal gas law in thermodynamic cycles
  • Explore methods for determining unknown parameters in thermodynamic problems
  • Investigate the significance of the specific heat ratio (k) in engine efficiency
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Students studying thermodynamics, mechanical engineers focusing on internal combustion engines, and anyone involved in analyzing or optimizing Otto Cycle performance.

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Homework Statement



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p1, V1, T1 and ε (compression ratio) are known

I need to find:
p2, p3, p4
T2, T3, T4
V2, V3, V4

but I don't know how to find p3, p4, T3, T4

Homework Equations



ε = V1 / V2
V1 = V4
V2 = V3
T1 * V1^(k - 1) = T2 * V2^(k - 1)
T3 * V3^(k - 1) = T4 * V4^(k - 1)
T1 / T4 = T2 / T3
p * V = R * T

R and k are also known

The Attempt at a Solution



V2 = V1 / ε
V3 = V2
V4 = V1

T2 = T1 * ε ^ (k - 1)

p2 = (R * T2) / V2

And this is where I got stuck
 
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The problem is under-defined. You need either P or T for one of the upper points.
For the process 1→2, use the other equation PVk=const to find P2.

ehild
 

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