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?

Question

Physics

Tatum Fowler

22 May, 20:41

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?

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Natalee · 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