Question

Air is compressed from 20 psia and 70°F to 150 psia in a compressor. The compressor is operated such that the air temperature remains constant. Calculate the change in the specific volume of air as it passes through this compressor. ​

Answer 1

Answer: -8.51 ft^3/lbm

Step-by-step explanation:

In this question, to find the change in volume, we will use the ideal gas law.

`\begin{aligned}&n_(1)=1 \text { mole }\\&\mathrm{P}_(1)=20 \mathrm{psia}\\&\mathrm{T}_(1)=70^(\circ) \mathrm{F}\\&T_(1)=(70+460)^(0) \mathrm{R}\\&v_(1)=\frac{\left(0.3704 \frac{psia \cdot_{\text { } ft^(3)}}{l \mathrm{lbm} \cdot R}\right)(70+460)^(0) \mathrm{R}}{20 \mathrm{psi}}\\&v_(1)=9.816 \frac{\mathrm{ft}^(3)}{\mathrm{lbm}}\end{aligned}`

`\begin{aligned}&\mathrm{n}_(2)=1 \text { mole } \\&\mathrm{P}_(2)=150 \mathrm{psia} \\&\mathrm{T}_(1)=\mathrm{T}_(2)=70^(0) \mathrm{~F} \\&\mathrm{~T}_(1)=\mathrm{T}_(2)=(70+460)^(0) \mathrm{R} \\&v_(2)=\frac{\left(0.3704 \frac{\text { psia} \cdot \mathrm{ft}^(3)}{\mathrm{lbm} \cdot R}\right)(70+460)^(0) \mathrm{R}}{150 \mathrm{psi}} \\&v_(2)=1.309 \frac{\mathrm{ft}{ }^(3)}{\mathrm{lbm}}\end{aligned}`