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Problem #2: Solution of Non-Linear Equations (4*2 = 8 marks) Source: Kiusalas, Ex. 20, p. 169 The figure on right shows the thermodynamics cycle of an engine. The efficiency of this engine for monoatomic gas is given by $\eta = \frac{\ln(T_2/T_1) - (1 - T_1/T_2)}{\ln(T_2/T_1) + (1 - T_1/T_2)/(\gamma - 1)}$ where T is the absolute temperature (°K), and $\gamma = 5/3$. Determine $T_2/T_1$ that results in 30% efficiency using MATLAB script by (a) Bisection method, (b) Newton-Raphson method.

          Problem #2: Solution of Non-Linear Equations (4*2 = 8 marks)
Source: Kiusalas, Ex. 20, p. 169
The figure on right shows the thermodynamics cycle of an engine.
The efficiency of this engine for monoatomic gas is given by
$\eta = \frac{\ln(T_2/T_1) - (1 - T_1/T_2)}{\ln(T_2/T_1) + (1 - T_1/T_2)/(\gamma - 1)}$
where T is the absolute temperature (°K), and $\gamma = 5/3$. Determine
$T_2/T_1$ that results in 30% efficiency using MATLAB script by
(a) Bisection method, (b) Newton-Raphson method.

Show more…

Problem #2: Solution of Non-Linear Equations (4*2 = 8 marks)
Source: Kiusalas, Ex. 20, p. 169
The figure on right shows the thermodynamics cycle of an engine.
The efficiency of this engine for monoatomic gas is given by
η = (ln(T2/T1) - (1 - T1/T2))/(ln(T2/T1) + (1 - T1/T2)/(γ - 1))
where T is the absolute temperature (°K), and γ = 5/3. Determine
T2/T1 that results in 30% efficiency using MATLAB script by
(a) Bisection method, (b) Newton-Raphson method.

Added by Paul H.

Calculus: Early Transcendentals

James Stewart 8th Edition

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Solved by Expert Adi S

Step 1

The efficiency equation is given as: n = ln(Tz/Ti) + (γ - 1)(Tz - Ti)/Ti where n is the efficiency, γ = 5/3, and we want to find Tz/Ti for 30% efficiency. So, we can rewrite the equation as: 0.3 = ln(Tz/Ti) + (2/3)(Tz - Ti)/Ti Now, let x = Tz/Ti. Then the Show more…

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Problem #Z: Solution of Non-Linear Equations (4*2 = 8 marks) Source: Kiusalas, Ex. 20, p. 169 The figure on the right shows the thermodynamic cycle of an engine. The efficiency of this engine for monoatomic gas is given by: In(Tz/T) - ( - T/T)n = In(Tz/Ti) + ( - T/T)y - 1 Heating at constant volume Isothermal expansion Volume reduced by cooling where T is the absolute temperature (Â°K), and v = 5/3. Determine Tz/Ti that results in 30% efficiency using MATLAB script by (a) Bisection method, (b) Newton-Raphson method:

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