a hypothetical device is supplied with 2kgs of air as t 400k

a hypothetical device is supplied with
2kg/s of air as t 400kpa and 300k. Two separate streams of air leave the device. each stream is at an ambient pressure of 100kpa and the made flow rate is the sane for both streams. The inventor claims that one of the exit streams is at 330k while the other is at 270k. The ambient environment is at 300k . Assume the heat transfer date is negligible. Determine whether such a device is possible. For heat capacity of air A=3.355,B=0.575×10^-3 ,C=0 , D=-0.016×10^5. The molar mass of air I\'d 28.851g/mol.
(thermodynamics)

(2 kgs) surface Hot air Hypothetical device Cold air u keys)

Solution

For air, gas constant R = 8314 / 28.851 = 288.17 J/kg-K

C_p / R = A + BT + CT² + D/T²

Entropy generation rate for the CV, S_gen = m3*s3 + m2*s2 - m1*s1

= m3*s3 + m2*s2 - (m2 + m3)*s1

= m3*(s3 - s1) + m2*(s2 - s1)

Now ds = (Cp / T) dT - (R/P) dP

ds = R*(A/T + B + CT + D/T³) dT - (R/P) dP

Integrating s2 - s1 = R*[A ln (T2 / T1) + B (T2 - T1) + C/2 (T2² - T1²) - D/2 (T2^-2 - T1^-2) ] - R ln (P2 / P1)

Putting values, we get

s2 - s1 = 496.16 J/kg-K

s3 - s1 = 293.25 J/kg-K

S_gen = 1*293.25 + 1*496.16

S_gen = 789.41 J/kg-K

Since S_gen > 0, the device is possible.