• Reversible Adiabatic Expansion (or compression) of an Ideal Gas

In an adiabatic expansion (V2 > V1), the gas cools (T2 > T1).
And in an adiabatic compression (V2 < V1), the gas heats up.
? ???
For an ideal gas (one mole) T =pV ? p2 = V1 ?? 11 ?=pV ?
? ??? pV 22
R ? ???V2
p1
pV ? is constant along a reversible adiabat
For an isothermal process T = constant ? pV = constant
5.60 Spring 2008 Lecture #5 page 2
p V2adiabat < V2isotherm
p1 because the gas cools during reversible adiabatic expansion
p2
V1 V2ad V2iso
•In an adiabatic expansion (V2 > V1), the gas cools (T2 > T1).
And in an adiabatic compression (V2 < V1), the gas heats up.
? ???
For an ideal gas (one mole) T =pV ? p2 = V1 ?? 11 ?=pV ?
? ??? pV 22
R ? ???V2
p1
pV ? is constant along a reversible adiabat
For an isothermal process T = constant ? pV = constant
5.60 Spring 2008 Lecture #5 page 2
p V2adiabat < V2isotherm
p1 because the gas cools during reversible adiabatic expansion
p2
V1 V2ad V2iso
•In an adiabatic expansion (V2 > V1), the gas cools (T2 > T1).
And in an adiabatic compression (V2 < V1), the gas heats up.
? ???
For an ideal gas (one mole) T =pV ? p2 = V1 ?? 11 ?=pV ?
? ??? pV 22
R ? ???V2
p1
pV ? is constant along a reversible adiabat
For an isothermal process T = constant ? pV = constant
5.60 Spring 2008 Lecture #5 page 2
p V2adiabat < V2isotherm
p1 because the gas cools during reversible adiabatic expansion
p2
V1 V2ad V2iso
•In an adiabatic expansion (V2 > V1), the gas cools (T2 > T1).
And in an adiabatic compression (V2 < V1), the gas heats up.
? ???
For an ideal gas (one mole) T =pV ? p2 = V1 ?? 11 ?=pV ?
? ??? pV 22
R ? ???V2
p1
pV ? is constant along a reversible adiabat
For an isothermal process T = constant ? pV = constant
5.60 Spring 2008 Lecture #5 page 2
p V2adiabat < V2isotherm
p1 because the gas cools during reversible adiabatic expansion
p2
V1 V2ad V2iso
•In an adiabatic expansion (V2 > V1), the gas cools (T2 > T1).
And in an adiabatic compression (V2 < V1), the gas heats up.
? ???
For an ideal gas (one mole) T =pV ? p2 = V1 ?? 11 ?=pV ?
? ??? pV 22
R ? ???V2
p1
pV ? is constant along a reversible adiabat
For an isothermal process T = constant ? pV = constant
5.60 Spring 2008 Lecture #5 page 2
p V2adiabat < V2isotherm
p1 because the gas cools during reversible adiabatic expansion
p2
V1 V2ad V2iso
•