Question

5.37 At steady state, a power cycle develops a power output of 10 kW while receiving energy by heat transfer at the rate of 10 kJ per cycle of operation from a source at temperature T. The cycle rejects energy by heat transfer to cooling water at a lower temperature of 300 K. If there are 100 cycles per minute, what is the minimum theoretical value for T, in K?

Answer 1

Answer: minimum theoretical value of T = 750k

Explanation:

Assuming the the cycle is reversible and is ideal then

Wnet/Qh = Nmin .... equa 1

Equation 1 can be rewritten as

(Th -TL)/ Th ...equation 2

Th= temp of hot reservoir

TL= temp of low reservoir= 300

Wnet = power generated=10kw

He = energy transfer=10kj per cycle

Qhe = power transfer = (100/60)*10Kj = 16.67kw

Sub into equat 1

Nmin = 10/16.67 = 0.6

Sub Nmin into equation 2

Th = -TL/(Nmin -1) = -300k/(0.6 - 1)

Th =750k