Question #115774

Air initially at 75 psia and 65 0F is compressed to a final pressure of 300 psia and temperature of 320 0F. Find the polytropic exponent for the process.

Expert's answer

Here in the given equation it is given that ,

"P_1=" "75 psia, T_1= 65 ^oF,P_2=300 psia, T_2= 320 ^oF"

we know that for polytropic process

"\\frac{T_2}{T_1}= (\\frac{P_2}{P_1})^{\\frac{n-1}{n}}"

"\\frac{320}{65}= (\\frac{300}{75})^{\\frac{n-1}{n}}"

4.923="(4)^{\\frac{n-1}{n}}"

On taking log both sides

log(4.923)= "(\\frac{n-1}{n})log 4"

0.692n=(n-1)0.602

0.692 n = 0. 602 n - .602

0.09 n= -.602

n= - 6.68 here n is the polytropic exponent

but for real condition polytropic exponent can not be negative

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