Carnot Cycle Applications

One-tenth kilogram of air as an ideal gas with k = 1.4 executes a Carnot refrigeration cycle, as shown in Fig. 5.16. The isothermal expansion occurs at −23°C with a heat transfer to the air of 3.4 kJ. The isothermal compression occurs at 27°C to a final volume of 0.01 m3. Using the results of Prob. 5.80 adapted to the present case, determine

(a) the pressure, in kPa, at each of the four principal states.

(b) the work, in kJ, for each of the four processes.

(c) the coefficient of performance.

Prob. 5.80

Carnot Cycle Applications

The pressure-volume diagram of a Carnot power cycle executed by an ideal gas with constant specific heat ratio k is shown in Fig. P5.80. Demonstrate that

(a) V4V2 = V1V3.

(b) T2/T3 = (p2/p3)(k-1)/k.

(c) T2/T3 = (V3/V2)(k-1).

Fig. P5.80

Fig. 5.16 p?v diagram for a Carnot gas refrigeration or heat pump cycle.

Step 1 of 6</p>

Consider of air executes a carnot refrigeration cycle in which the isothermal expansion occurs at with a heat transfer to the air of and the isothermal compression occurs at to a final volume of .

We need to find out the pressure at each of the four principal states, the work for each of the four processes and the coefficient of performance.

Step 2 of 6</p>

We have,

And,

a) Using the ideal gas equation,

For process ,

Step 3 of 6</p>

The volume at is,

For process

SO,

So,

Thus,