Isothermal Gas Expansion

Maximum work delivered to surroundings for isothermal gas
V2 expansion is obtained using a reversible path
For ideal gas: V nRT V2 p2
w =??V12V dV =?nRT lnV1 =nRT ln p1
rev
-rev p p2 p1 V1
5.60 Spring 2008 Lecture #3 page 3
The Internal Energy U dU = d-q +d-w (First Law) dU =CpathdT ?pextdV
And ( , ? dU =???U ?? dT +??U ?? dV
UTV ) ??T ?V ???V ?T
Some frequent constraints:
•
Reversible ? dU = d-qrev +d-wrev = d-qrev – pdV (p = pext )
•
Isolated ?d-q =d-w = 0
reversible
•
Adiabatic ?d-q = 0 ? dU = d-w = -pdV
•
Constant V ? w = 0 ? dU = d-qVConstant V
dU =???U ??dT +???U ????V dV ??T ?V ?T
but also
? d-qV =?????TU ???V dT
d-qV =CVdT ? ??? ??TU ???V =CV very important result!!
So dU =C dT +???U ?? dV V ??V ?T what is this?Maximum work delivered to surroundings for isothermal gas
V2 expansion is obtained using a reversible path
For ideal gas: V nRT V2 p2
w =??V12V dV =?nRT lnV1 =nRT ln p1
rev
-rev p p2 p1 V1
5.60 Spring 2008 Lecture #3 page 3
The Internal Energy U dU = d-q +d-w (First Law) dU =CpathdT ?pextdV
And ( , ? dU =???U ?? dT +??U ?? dV
UTV ) ??T ?V ???V ?T
Some frequent constraints:
•
Reversible ? dU = d-qrev +d-wrev = d-qrev – pdV (p = pext )
•
Isolated ?d-q =d-w = 0
reversible
•
Adiabatic ?d-q = 0 ? dU = d-w = -pdV
•
Constant V ? w = 0 ? dU = d-qVConstant V
dU =???U ??dT +???U ????V dV ??T ?V ?T
but also
? d-qV =?????TU ???V dT
d-qV =CVdT ? ??? ??TU ???V =CV very important result!!
So dU =C dT +???U ?? dV V ??V ?T what is this?Maximum work delivered to surroundings for isothermal gas
V2 expansion is obtained using a reversible path
For ideal gas: V nRT V2 p2
w =??V12V dV =?nRT lnV1 =nRT ln p1
rev
-rev p p2 p1 V1
5.60 Spring 2008 Lecture #3 page 3
The Internal Energy U dU = d-q +d-w (First Law) dU =CpathdT ?pextdV
And ( , ? dU =???U ?? dT +??U ?? dV
UTV ) ??T ?V ???V ?T
Some frequent constraints:
•
Reversible ? dU = d-qrev +d-wrev = d-qrev – pdV (p = pext )
•
Isolated ?d-q =d-w = 0
reversible
•
Adiabatic ?d-q = 0 ? dU = d-w = -pdV
•
Constant V ? w = 0 ? dU = d-qVConstant V
dU =???U ??dT +???U ????V dV ??T ?V ?T
but also
? d-qV =?????TU ???V dT
d-qV =CVdT ? ??? ??TU ???V =CV very important result!!
So dU =C dT +???U ?? dV V ??V ?T what is this?