Modern Engineering Thermodynamics

Problems 527
7. The thermal efficiency of a Stirling cold ASC external combustion engine is
ðη T Þ Stirling
= 1 − T L /T H = 1 − T 2 /T 1 = 1 − T 3 /T 4
cold ASC
8. The thermal efficiency of an Ericsson cold ASC external combustion engine is
ðη T Þ Ericsson
= 1 − T L /T H = 1 − T 2 /T 1 = 1 − T 3 /T 4
cold ASC
9. The thermal efficiency of a Lenoir cold ASC internal combustion engine is
ðη T Þ Lenoir
= 1 − kT 3 ðCR − 1Þ/ ðT 1 − T 4 Þ
cold ASC
10. The thermal efficiency of a Brayton cold ASC external combustion engine is
ðη T Þ Brayton
= 1 − T 3 /T 4s = 1 − PR ð1−kÞ/k = 1 − CR 1−k
cold ASC
11. The thermal efficiency of an Otto cold ASC internal combustion engine is
ðη T Þ Otto
= 1 − T 3 /T 4s = 1 − PR ð1−kÞ/k = 1 − CR 1−k
cold ASC
12. The thermal efficiency of a Diesel cold ASC internal combustion engine is
ðη T Þ Diesel
= 1 − CR1−k ðCO k − 1Þ
kðCO − 1Þ
cold ASC
where CO is the cutoff ratio of the engine.
13. The indicated cold ASC power output of either an Otto or Diesel cycle engine is
ð
ð _W 1 Þ out =
η TÞ ASC
_Q/ _m ðDNp fuel 1 /CÞ
ðA/FÞðRT 1 ÞðCR − 1Þ
where D is the engine’s total displacement, N is the engine speed in revolutions per time, C is the number
of crankshaft revolutions per power stroke, and A/F is the air/fuel ratio of the engine.
14. The thermal efficiency of an Atkinson cold ASC internal combustion engine is
ðη T Þ Atkinson
cold ASC
kðER − CRÞ
= 1 −
ER k − CR k
where ER is the isentropic expansion ratio v 2s /v 1 and CR is the isentropic compression ratio v 3 /v 4s .
15. The actual thermal efficiency of any of the cycles discussed in this chapter is
where η m is the mechanical efficiency of the engine.
ðη T Þ actual = ðη m Þðη T Þ ASC
Problems (* indicates problems in SI units)
1. The duty of a 1718 Newcomen engine was found to be 4.30
million. Determine its thermal efficiency (%).
2. In 1767, John Smeaton measured the performance of a
particularly efficient Newcomen engine that had a 42.0-inch
diameter piston and found that it produced 16.7 net horsepower
with a duty of 7.44 million. Determine (a) the thermal efficiency
of the engine and (b) the boiler heat input rate.
3. In 1767 John Smeaton measured the performance of a
Newcomen engine with a 60.0-inch diameter piston and found
that it produced 40.8 net horsepower with a duty of 5.88
million. Determine (a) the thermal efficiency of this engine and
(b) its boiler heat input rate.
4. In 1767, John Smeaton measured the performance of a
Newcomen engine with a 75.0-inch diameter piston and found
that it produced 37.6 net horsepower with a duty of 4.59
million. Determine (a) the thermal efficiency of this engine and
(b) the boiler heat input rate.
5. In 1772, John Smeaton used the results of his tests on various
existing Newcomen cycle engines to design and build his own
atmospheric steam engine. It had a 52.0-inch diameter piston
with a 7.0 ft stroke and operated at 12.5 strokes per minute
with a mean effective pressure of 7.50 lbf/in 2 . It produced a
remarkably high duty of 9.45 million. Determine the (a)
thermal efficiency, (b) the horsepower output, and (c) the boiler