- #1
mclame22
- 13
- 0
Homework Statement
Show that the net work done by the otto engine per cycle is
Cv(Tc - Tb)(1 - Ta/Tb)
PV diagram:
[PLAIN]http://www.antonine-education.co.uk/physics_a2/options/module_7/topic_4/Otto_indic.gif [Broken]
Homework Equations
Work done by a kmole of gas expanding irreversibly and adiabatically from
P1 V1 T1 to P2 V2 T2:
= (P1V1 - P2V2)/(γ - 1) = R(T1 - T2)/(γ - 1)
The Attempt at a Solution
The only work done by the otto engine is during the adiabatic expansions/compressions. So the work done by the gas from point A to point B is
= R(Ta - Tb)/(γ - 1)
Likewise, the work done by the gas from point C to point D is
= R(Tc - Td)/(γ - 1)
So the net work done by the gas will be
= R(Ta - Tb)/(γ - 1) + R(Tc - Td)/(γ - 1)
= (R/(γ - 1))(Ta - Tb + Tc - Td)
= Cv[(Tc - Tb) + Ta - Td]
Here I get stuck. I don't see why the answer doesn't have a Td term. Have I gone wrong somewhere?
Last edited by a moderator: