process
DESCRIPTION
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Thermodynamic Processes
• States of a thermodynamic system can be changed by interacting with its surrounding through work and heat. When this change occurs in a system, it is said that the system is undergoing a process.
• A thermodynamic cycle is a sequence of different processes that begins and ends at the same thermodynamic state.
• Some sample processes: Isothermal process: temperature is constant T=C Isobaric process: pressure is constant, P=C Isentropic process: entropy is constant, s=C Constant-volume process, v=C Adiabatic process: no heat transfer, Q=0
Process-1• Use ideal gas assumption (closed system):
2
1
2 1
1 2
Isothermal process: T=constantEnergy balance U=Q-W, for ideal gas U= H=0since both are functions of temperature only
Q=W, W= P
ln ln
Isobaric process:
mRT dVdV dV mRTV V
V PmRT mRTV P
2
2 11
2 1 2 1 2 1
2 2 1 1 2 1
P=constant
U=Q-W, W= PdV=P dV=P(V )
( ) ( ) ( )( ) ( )
V
Q U P V V U U P V VU PV U PV H H H
Process-2
v
v
Constant volume process: V=constant
Q-W= U, W= 0, no work done
Q= U=m u=m c
Adiabatic process: Q=0Q-W= U, -W= U- W=dU (infinitesimal increment of work and energy)
dU+PdV=0, mc 0
v
PdV
dT
mRTdT dVV
c
v
2 2 2 1 1
1 1 1 2 2
1
0, , integrate and assume
c =constant
ln ln ,
v
vv
R kc
cRT dT dVdT dVV R T V
c T V T V VR T V T V V
Process-3
2 1
1 2
1 1 2
2 2 1
2 1 2 2
1 2 1 1
2 2 2 1
1 1 1
( 1)
1
1 1
, from ideal gas relation
PV=RT, , substitute
, multiply from both sides
,k
k
k
k k
T VT V
V T PV T P
T T P TT T P T
T P P VT P P
and
2
1 1 2 2kAlso and tan
For an ideal gas undergoing adiabatic process
k
k
k
V
PV PV pV cons t
Process-4
Polytropic Process: its P-V relation can be expressed asPVn = constant, where n is a constant for a specific process
Isothermal, T=constant, if the gas is an ideal gas then PV=RT=constant, n=1 Isobaric, P=constant, n=0 (for all substances) Constant-volume, V=constant, V=constant(P)(1/n), n= (for all substances) Adiabatic process, n=k for an ideal gas
1 1 2 2
2 2
1 11 1
21 11 1 2 2 1 1
1 1 2 11
( )
( )( ) ( )1 1
n n n
n n
nn n n n
PV PV PV
W PdV PV V dV
PV PV PVPV V dV V Vn n