An air-standard Otto cycle works on of a diatomic ideal gas with constant heat capacities

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

Thermal Physics, Ch The second law, entropy and irreversibility

Problem

An air-standard Otto cycle works on

0.0200\,\mathrm{mol}

of a diatomic ideal gas with constant heat capacities,

C_V = \tfrac52 nR

and

\gamma = 7/5

. The compression ratio is

r = V_1/V_2 = 8.00

. The four legs are:

1 \to 2

: reversible adiabatic compression from

T_1 = 300\,\mathrm{K}

;

2 \to 3

: constant-volume heating in which

400\,\mathrm{J}

of heat is delivered to the gas from a combustion-gas source at

1900\,\mathrm{K}

;

3 \to 4

: reversible adiabatic expansion back to the volume

V_1

;

4 \to 1

: constant-volume cooling, the gas being put in thermal contact with the atmosphere, a reservoir at

300\,\mathrm{K}

, until it is back at state 1. Take

R = 8.314\,\mathrm{J\,mol^{-1}\,K^{-1}}

and treat the atmosphere at

300\,\mathrm{K}

as the coldest body available. ((a)) Find

T_2

T_3

and

T_4

. ((b)) Find the heat rejected on

4 \to 1

and the efficiency of the cycle. ((c)) Find the efficiency of a reversible engine working between the highest and lowest temperatures the gas reaches. ((d)) Draw up the entropy ledger for the leg

4 \to 1

(gas column, reservoir column) and give the entropy created per cycle. ((e)) Find the lost work per cycle on that leg. ((f)) Evaluate the sum of

Q/T

round the whole cycle, using the temperature of the body that supplies or receives each heat, and check the Clausius inequality.

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