From Robert Balmer\'s Modern Engineering Thermodynamics, Chapter 9, Problem 24:

Question

From Robert Balmer's Modern Engineering Thermodynamics, Chapter 9, Problem 24:

A solar concentrating heat exchanger system directs sunlight onto a large, straight pipe. The pipe receives 153.616 Btu/h per foot of length. If water enters the pipe at 50.0 lbm/h as saturated liquid at 300°F and is heated isothermally so that it leaves as vapor at 20.0 psia, then:

a. How long is the pipe for steady state, steady flow conditions?
b. What is the rate of entropy production?
c. Show whether this system violates the second law of thermodynamics.

An explanation would be helpful, so I can understand the process. I'm trying to use Qdot - Wdot + mdot(hin - hout) for part a, but the numbers don't seem right. Any help would be appreciated.

Explanation / Answer

a) Q recieved for L feet length of pipe = 153.616 Btu/h x L

mass flow rate = m_rate = 50 lbm/h

At T1 = 300 F , for staurated liquid:

h1 = 272.31 Btu/lb and v1 =1.2 ft^3/lbm

and at T2 = 300 F (isothermal) and P2 = 20.0 psia,

h2 = 1194.036 Btu/lb and v2 = 22.36 ft^3/kg

Q -W = m_rate x (h2 - h1)

W done = m_rate x R x T(in kelvin) ln v2/v1

R = 287.05 J/Kg.K

after putting in proper units. calculate W done

Then, putting in formula:

153.616 Btu/h x L - W = m_rate (h2 - h1)

here h2,h1,W are known. Calculate L from here

b) entropy produced will be = Q/T

after calculating L, put it in Q to get Q and divide it by temp to get entropy .(temp = 300 F = constant)

c) no it doesnt violates.

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