Question

Optimum Compression ratio for maximum specific output for ideal gas (air) turbine plant operating at initial temperature of 290K and maximum temperature of 1000K, is closure to

Answer 1

Answer: The required optimum compression ratio is 21.94.

Step-by-step explanation:

As we know that compression ratio $r=\frac{v_2}{v_1}$

And, η$=1-\frac{1}{r^{k-1} }$

Where, $k=1.4$ for diatomic molecule.

We also know, if temperatures are given, then

η$=1-\frac{T_2}{T_1}$

$1-\frac{T_2}{T_1} =1-\frac{1}{r^{1.4-1} }\\1-\frac{290}{1000} =1-\frac{1}{r^{0.4} }\\0.71=1-\frac{1}{r^{0.4}}\\\frac{1}{r^{0.4} }=0.29\\3.44=r^{0.4} \\r=21.94$

Therefore, Optimum Compression ratio for maximum specific output for ideal gas (air) turbine plant operating at initial temperature of 290K and maximum temperature of 1000K, is closure to 21.94.

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Answer 2

Given:

Gas power plant working medium - ideal gas

initial temperature 290k    maximum temperature 1000k

To find:

Optimum compression ratio for a gas power plant

Solution:

Optimum compression ratio is defined as the value of compression ratio at which maximum work output is obtained.

Conditions for maximum workdone

$T_{2} = T_{4} = \sqrt{T_{1}T_{3} }$

we know that for a gas power plant ,

$r_{p} =(\frac{T_{2} }{T_{1} }) ^{\frac{\alpha }{\alpha -1} }$

$T_{2 = \sqrt{T_{3} T_{1} }$

$T_{3} = T_{max} and T_{1} = T_{min}$

substitute  in the formula,

$r_{opt} = \frac{T_{3} }{T_{1} }} ^{ \frac{\alpha }{2(\alpha-1) }$

$\alpha$ is poisson's ratio = 1.4 for ideal gas

Substitute the values given in the question to the formula of optimum compression ratio.

$T_{3} = 1000K \\ T_{1} = 290K$

$r_{opt} = 8.69$

Optimum compression ratio for maximum specific output for ideal gas power plant is equal to 8.69