Ideal Isometric Gas System - Otto Cycle

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Process 1-2

Isentropic Compression

\( W = \frac{P_2 V_2 - P_1 V_1}{1- \gamma} \)

\( Q = 0 \)

Process 2-3

Isometric Heat Transfer

\( W = 0 \)

\( Q = m C_v \Delta T = \Delta U_{23} \)

Process 3-4

Isentropic Expansion

\( W = \frac{P_4 V_4 - P_3 V_3}{1- \gamma} \)

\( Q = 0 \)

Process 4-1

Isometric Heat Transfer

\( W = 0 \)

\( Q = m C_v \Delta T = \Delta U_{41} \)


Compression Ratio

\( r_v = \frac{v_1}{v_2} = \frac{v_4}{v_3} \)


Thermal Efficiency

\( \eta _{th} = \frac{W_{net}}{Q_{in}} = 1 - \frac{Q_{out}}{Q_{in}} ; Q = m C_v \Delta T \)

Air Standard Efficiency

\( \eta _{ASE} = 1 - \frac{1}{r_v ^{\gamma -1}} \)