Solution Found!
Air is compressed in an isentropic compressor from 15 psia
Chapter 7, Problem 87P(choose chapter or problem)
Air is compressed in an isentropic compressor from 15 psia and \(70^{\circ} \mathrm{F}\) to 200 psia. Determine the outlet temperature and the work consumed by this compressor per unit mass of air.
Questions & Answers
QUESTION:
Air is compressed in an isentropic compressor from 15 psia and \(70^{\circ} \mathrm{F}\) to 200 psia. Determine the outlet temperature and the work consumed by this compressor per unit mass of air.
ANSWER:
Step 1 of 2
Obtain properties of air at an average temperature of \(400^{\circ} \mathrm{F}\) from table A-2E, “ideal gas specific heat of gases” in the textbook.
Specific heat at constant pressure, \(c_p=0.245\mathrm{\ Btu}/\mathrm{lbm}\cdot R)
Specific heat ratio, k = 1.389
Find the temperature at the exit of the compressor by using the following isentropic relation:
\(\frac{T_{2}}{T_{1}}=\left(\frac{P_{2}}{P_{1}}\right)^{\frac{k-1}{k}}\)
Here, \(P_{1}\) is the compressor inlet pressure, \(P_{2}\) is compressor exit pressure, \(T_{1}\) is compressor inlet temperature, and \(T_{2}\) is the compressor exit temperature.
Substitute (70 + 459.67) R for \(T_{1}\), 15 psia for \(P_{1}\), 200 psia for \(P_{2}\), and 1.389 for k.
\(\begin{array}{l}T_2=T_1\times\left(\frac{P_2}{P_1}\right)^{\frac{k-1}{k}}\\ T_2=(70+459.67)\times\left(\frac{200}{15}\right)^{\frac{1.389-1}{1.389}}\\ T_2=1094.6\ R\\ T_2\approx1095\ R \end{array}\)
Therefore, the outlet temperature of the air is 1095 R.