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Determine the mean effective pressure of an ideal Otto Cycle that uses air as the working fluid; its state at the beginning of the compression is 14 psia and 60oF; its temperature at the end of the combustion is 1500oF; and its compression ratio is 9. Use constant specific heats at room temperature.

Respuesta :

batolisis

Answer:

31.282 psia

Explanation:

Calculate the mean effective pressure of an ideal Otto cycle

Given data:

compression ratio = 9

inlet pressure ( P1 ) = 14 psia

Initial temperature ( T1 ) = 60°F = 520 R

Final/maximum temp ( T3 ) = 1500°F = 1960 R

using the constant specific heats at room temperature

attached below is the detailed solution

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The mean effective pressure of the ideal Otto Cycle that uses air as the working fluid is; 31.28 psia

We are given;

Initial pressure; P₁ = 14 psia

Initial temperature; T₁ = 60°F = 520 R

Maximum temperature; T₃ = 1500°F = 1960 R

Compression ratio = 9

From tables, the specific heat capacities and constants are;

c_v = 0.171 btu/lbm.R

c_p = 0.24 btu/lbm.R

R = 0.3704 btu/lbm.R

ratio of specific heats; k = 1.4

Let us first calculate the initial volume from the formula;

V₁ = RT₁/P₁

V₁ = (0.3704 * 520)/14

V₁ = 13.7577 ft³/lb.m

  • Compression ratio is; V₁/V₂ = 9

Thus;

V₂ = V₁/9

V₂ = 13.7577/9

V₂ = 1.5286 ft³/lb.m

  • To get the temperature T₂, we will use the formula;

T₂ = T₁(V₁/V₂)^(k - 1)

T₂ = 520(9)^(1.4 - 1)

T₂ = 1252.277 R

Similarly;

T₄ = T₃/9

T₄ = 1960/(9^(1.4 - 1))

T₄ = 813.87 R

  • Formula for heat entering and heat exiting are;

Q_in = c_v(T₃ - T₂)

Q_in = 0.171(1960 - 1252.277)

Q_in = 121.02 btu/lbm

Q_out = c_v(T₄ - T₁)

Q_out = 0.171(813.87 - 520)

Q_out = 50.251 btu/lbm

  • Net work done is given by;

W_net = Q_in - Q_out

W_net = 121.02 - 50.251

W_net = 70.769 btu/lbm

Formula for the mean effective pressure is;

mean effective pressure = W_net/(V₁ - V₂)

mean effective pressure = 70.769/(13.7577 - 1.5286)

mean effective pressure = 5.7869 btu.ft³

Converting to psia gives;

Mean effective pressure = 31.28 psia

Read more about compression ratio at; https://brainly.com/question/16014998

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