Question

Air in a piston/cylinder goes through a Carnot cycle with the P-v diagram . The high and low temperatures are 600 K and 300 K respectively. The heat added at the high temperature is 250 kJ/kg and the lowest pressure in the cycle is 75 kPa. Find the specific volume and pressure after heat rejection and the net work per unit mass.

Answer 1

qH = 250 kJ/kg , TH = 600 K, TL = 300 K, P3 = 75 kPa

The states as

1 : 600 K , 2: 600 K, 3: 75 kPa, 300 K 4: 300 K

Since this is a Carnot cycle and we know the temperatures the efficiency is

η = 1 − TL/TH = 1 - 300/600 = 0.5

and the net work becomes

wNET = ηqH = 0.5 × 250

= 125 kJ/kg

The heat rejected is

qL = qH – wNET = 125 kJ/kg

After heat rejection

qL = RTL ln (v3/v4)

v3 = RT3 / P3 = 0.287 x 300 / 75 = 1.148 m3/kg

v4 = v3 exp(-qL/RTL) = 1.148 exp(−125/0.287 × 300) = 0.2688 m3/kg

P4 = RT4 / v4 = 0.287 × 300 / 0.2688 = 320 kPa