Internal Energy(U)
(1)ΔU =ΔQv=nCv T=n f R ΔT
2
Work done from P-V Graph Equation of state
PV = constant
04
ΔU Compression -1
nRΔT=Δ(PV) TV = constant
= γ -1 γ-1 Adiabatic
-1 ΔV=0 o
[
=PfVf-PiVi ΔQv p PT =constant equatio
γ-1 othermal
Isochoric
(Internal Energy is only the function of Work d
Work done by the gas
temperature of the gas) Area=W
p W=-Δ U=nCv(T1-T2) ΔV=0=
f specific
=n2 R(Ti-Tf)
v Isobaric
=> Q=ΔU+ W Area under P-V diagram gives V W = nR
-1 (Ti-Tf)
=
First law of T.D work done by the gas
Q, path functions Wadaibatci > Wsiothermal > Wsiobarci > Wsiochorci
PiVi-PfVf
ΔU state function W=
-1
1 Isobaric process Cyclic process
W1=/ W2 Slope of adiabatic process ‘De
• W=are inside the graph = x slope of isothermal process
Q1=
/ Q2 hea
state A state B
ΔU1=ΔU2=UB-UA
• For clockwise process, W=-ve specific heat of gas =>
C=0
p • For anti-clockwise process, W=+ve C= Q Q =0 High
Δt
2
W=P(V2-V1) temp.
C=0
02
P2 P2
P1
P1
Isothermal process
Isothermal process = ΔT=0 > ΔU=0 V1 V2
V1 V2 V1 V2
Cyclic process A Isochoric process W=π4(P2-P1)(V2-V1) 1
W= 2 (P2-P1)(V2-V1)
=>ΔT=0=>ΔU=0
eg:- perfectly conducting
A B C D A B P slow process
ΔU=UA-UA=0 P2
Q= Δ U+W
W=PΔV=0
D Q= W
C P1
p Low
V
equation of states =>PV=Constant
P V =P V
WORK V1 V2
Workdone by the gas
1 1 2 2
effic
Work done: W=(P2-P1)(V2-V1)
V2
path function
W=F.dx=Pdv V W=2.303 nRT log V1 ( η=
Unit: Joule(J)
P1
p A B
Thermodynamic processes
W=2.303 nRT log ( P2 η =
carnot
1
Sign Convention Slope:
01
+ve
Q W1 ηm
Slope of adiabatic process
W W
p A V
B = slope of isothermal process
System System Adiabatic process
-ve +ve A B specific heat C=
(compressive) (expansion) 2 p W1=
/ W2 Q=0 [no exchange of heat]
work done W2
03 Carn
work done on the gas
by the gas -ve
Q W1> W2
Work Heat V
V Rapid or spontaneous
(1)ΔU =ΔQv=nCv T=n f R ΔT
2
Work done from P-V Graph Equation of state
PV = constant
04
ΔU Compression -1
nRΔT=Δ(PV) TV = constant
= γ -1 γ-1 Adiabatic
-1 ΔV=0 o
[
=PfVf-PiVi ΔQv p PT =constant equatio
γ-1 othermal
Isochoric
(Internal Energy is only the function of Work d
Work done by the gas
temperature of the gas) Area=W
p W=-Δ U=nCv(T1-T2) ΔV=0=
f specific
=n2 R(Ti-Tf)
v Isobaric
=> Q=ΔU+ W Area under P-V diagram gives V W = nR
-1 (Ti-Tf)
=
First law of T.D work done by the gas
Q, path functions Wadaibatci > Wsiothermal > Wsiobarci > Wsiochorci
PiVi-PfVf
ΔU state function W=
-1
1 Isobaric process Cyclic process
W1=/ W2 Slope of adiabatic process ‘De
• W=are inside the graph = x slope of isothermal process
Q1=
/ Q2 hea
state A state B
ΔU1=ΔU2=UB-UA
• For clockwise process, W=-ve specific heat of gas =>
C=0
p • For anti-clockwise process, W=+ve C= Q Q =0 High
Δt
2
W=P(V2-V1) temp.
C=0
02
P2 P2
P1
P1
Isothermal process
Isothermal process = ΔT=0 > ΔU=0 V1 V2
V1 V2 V1 V2
Cyclic process A Isochoric process W=π4(P2-P1)(V2-V1) 1
W= 2 (P2-P1)(V2-V1)
=>ΔT=0=>ΔU=0
eg:- perfectly conducting
A B C D A B P slow process
ΔU=UA-UA=0 P2
Q= Δ U+W
W=PΔV=0
D Q= W
C P1
p Low
V
equation of states =>PV=Constant
P V =P V
WORK V1 V2
Workdone by the gas
1 1 2 2
effic
Work done: W=(P2-P1)(V2-V1)
V2
path function
W=F.dx=Pdv V W=2.303 nRT log V1 ( η=
Unit: Joule(J)
P1
p A B
Thermodynamic processes
W=2.303 nRT log ( P2 η =
carnot
1
Sign Convention Slope:
01
+ve
Q W1 ηm
Slope of adiabatic process
W W
p A V
B = slope of isothermal process
System System Adiabatic process
-ve +ve A B specific heat C=
(compressive) (expansion) 2 p W1=
/ W2 Q=0 [no exchange of heat]
work done W2
03 Carn
work done on the gas
by the gas -ve
Q W1> W2
Work Heat V
V Rapid or spontaneous