A brochure for a road car states: "Our petrol engine has a compression ratio of to

PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · The laws of thermodynamics · The laws of thermodynamics

Thermal Physics, Ch Internal-combustion cycles and indicator diagrams

Problem

A brochure for a road car states: "Our petrol engine has a compression ratio of

11.0

1

. Air-standard analysis with

\gamma = 1.4

gives a thermal efficiency of

62\%

, so

62\%

of the heat supplied to the working gas is delivered as work at the crankshaft. With a peak cycle temperature of

2200\ \mathrm{K}

and air drawn in at

300\ \mathrm{K}

, this is within a whisker of the Carnot limit." Take the air-standard Otto cycle as defined in this chapter: a fixed mass of air treated as an ideal gas with constant heat capacities, taken quasistatically round a closed cycle with the burn replaced by heat added at constant volume and the exhaust by heat removed at constant volume, and with friction and heat leaks absent. ((a)) Check the

62\%

figure by computing the air-standard Otto efficiency at

r = 11.0

with

\gamma = 1.4

. ((b)) Compute the Carnot efficiency of a reversible engine working between

300\ \mathrm{K}

and

2200\ \mathrm{K}

, and say whether the brochure's last sentence stands. ((c)) The middle sentence contains the brochure's main error. State it, and name three replacements the air-standard idealisation makes, saying in each case which way it pushes the computed efficiency.

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