Question

At steady state, a thermodynamic cycle operating between hot and cold reservoirs at 1000 K and 500 K, respectively, receives energy by heat transfer from the hot reservoir at a rate of 1500 kW, discharges energy by heat transfer to the cold reservoir, and develops power at a rate of (a) 1000 kW, (b) 750 kW, (c) 0 kW. For each case, apply Eq. 5.13 on a time-rate basis to determine whether the cycle operates reversibly, operates irreversibly, or is impossible.

Answer 1

Answer:

a. impossible

b. possible and reversible

c. possible and irreversible

Explanation:

a. 1000kw

Qh - Wnet

we have

QH = 1500

wnet = 1000

1500 - 1000

= 500kw

σcycle = $-[\frac{QH}{TH} -\frac{QC}{TC} ]$

Qh = 1500

Th = 1000

Tc = 500

Qc = 500

$-[\frac{1500}{1000} -\frac{500}{500} ]$

solving this using LCM

= -0.5

the cycle is impossible since -0.5<0

b. 750Kw

Qc = 1500 - 750

=750Kw

Qh = 1500

Th = 1000

Tc = 500

Qc = 750

σ-cycle

$-[\frac{1500}{1000} -\frac{750}{500} ]\\= 1.5 -1.5\\= 0$

This cycle is possible and it is also reversible

c. 0 kw

Qc = 1500-0

= 1500

Qh = 1500

Th = 1000

Tc = 500

Qc = 1500

σ- cycle

$-[\frac{1500}{1000} -\frac{1500}{500} ]\\-(1.5-3)\\-(-1.5)\\= 1.5$

1.5>0

so this cycle is possible and irreversible