7.29 A gearbox operating at steady state receives 4 hp along the input shaft and delivers 3 hp along the output shaft. The outer surface of thegearbox is at 130°F. For the gearbox,(a) determine, in Btu/s, the rate of heat transfer and(b) perform a full exergy accounting, in Btu/s, of the input power. Let To 70°F.

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Asked Sep 11, 2019
7.29 A gearbox operating at steady state receives 4 hp along the input shaft and delivers 3 hp along the output shaft. The outer surface of the
gearbox is at 130°F. For the gearbox,
(a) determine, in Btu/s, the rate of heat transfer and
(b) perform a full exergy accounting, in Btu/s, of the input power. Let To 70°F.
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7.29 A gearbox operating at steady state receives 4 hp along the input shaft and delivers 3 hp along the output shaft. The outer surface of the gearbox is at 130°F. For the gearbox, (a) determine, in Btu/s, the rate of heat transfer and (b) perform a full exergy accounting, in Btu/s, of the input power. Let To 70°F.

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check_circleExpert Solution
Step 1

(a)

Write the expression for exergy balance.

dE
out
in
dt
dE
=0)
(Since the gear box is operating in steady state, so
dt
ww.
0 WotWn Q
out
in
Q3 hp 4 hp
2545 Btu/hr
1hp
(-1hp)
1hr
=(-2545 Btu/hr
3600s
=-0.7069 Btu/s
Thus, the rate of heat transfer is -0.7069 Btu/s.
wwww
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dE out in dt dE =0) (Since the gear box is operating in steady state, so dt ww. 0 WotWn Q out in Q3 hp 4 hp 2545 Btu/hr 1hp (-1hp) 1hr =(-2545 Btu/hr 3600s =-0.7069 Btu/s Thus, the rate of heat transfer is -0.7069 Btu/s. wwww

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Step 2

(b)

Write the expression for exergy rate interring the system.

Е — W.
in
in
Exn = 4 hp
2545 Btu/hr
1hp
(4 hp)
1hr
= (10180 Btu/hr )\ 3600 s
=2.8277 Btu/s
Thus, the exergy rate entering the system is 2.827 Btu/s
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Е — W. in in Exn = 4 hp 2545 Btu/hr 1hp (4 hp) 1hr = (10180 Btu/hr )\ 3600 s =2.8277 Btu/s Thus, the exergy rate entering the system is 2.827 Btu/s

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Step 3

Write the expression for exergy ...

E W
out
out
3 hp
'out
2545 Btu/hr
-(3 hp)
1hp
1hr
=(7635 Btu/hr)
3600 s
-2.120 Btu/s
Thus, the exergy rate entering the system is 2.120 Btu/s
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E W out out 3 hp 'out 2545 Btu/hr -(3 hp) 1hp 1hr =(7635 Btu/hr) 3600 s -2.120 Btu/s Thus, the exergy rate entering the system is 2.120 Btu/s

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