Thermo Equation Sheet
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2Thermodynamics (EGGN 371)
Equation Sheet
Air Standard
Cold Air Standard
Process
(variable specific
(const. specific heats)
heats)
OTTO
1-2
isentropic compression
(
k
) 1
−
v
⎛
⎞
v
⎛
⎞
2
v
v
⎜ ⎜
⎟ ⎟
T
T
1
=
⎜ ⎜
⎟ ⎟
=
r
r
v
2
1
2
1
v
⎝
⎠
1
⎝
⎠
2
2-3
const. v heat addition
q
u
u
q
C
(
T
T
)
=
−
=
−
in
3
2
in
v
3
2
3-4
isentropic expansion
(
k
) 1
−
v
⎛
⎞
v
⎛
⎞
v
v
4
⎜ ⎜
⎟ ⎟
T
T
3
=
⎜ ⎜
⎟ ⎟
=
r
r
v
4
3
4
3
v
⎝
⎠
3
⎝
⎠
4
4-1
const. v heat rejection
q
u
u
q
C
(
T
T
)
=
−
=
−
out
4
1
out
v
4
1
q
v
v
1 (
k
)
1
r
−
η
=
−
out
1
4
= 1
r =
r =
otto
η
−
otto
q
v
v
in
2
3
DIESEL
1-2
isentropic compression
(
k
) 1
−
v
⎛
⎞
v
⎛
⎞
v
v
2
⎜ ⎜
⎟ ⎟
1
=
T
T
⎜ ⎜
⎟ ⎟
=
r
r
v
2
1
2
1
v
⎝
⎠
1
⎝
⎠
2
2-3
const. P heat addition
q
h
h
q
C
(
T
T
)
=
−
=
−
in
3
2
in
p
3
2
3-4
isentropic expansion
(
k
) 1
−
v
⎛
⎞
v
⎛
⎞
4
v
v
⎜ ⎜
⎟ ⎟
T
T
3
=
⎜ ⎜
⎟ ⎟
=
r
r
v
4
3
4
3
v
⎝
⎠
3
⎝
⎠
4
4-1
const. V heat rejection
q
u
u
q
C
(
T
T
)
=
−
=
−
out
4
1
out
v
4
1
q
v
k
r
1
⎡
⎤
−
out
1
= 1
r =
η
1 (
k
)
−
c
1
r
−
η
=
−
diesel
⎢
⎥
q
v
diesel
k
(
r
) 1
−
in
2
⎣
⎦
c
BRAYTON
1-2
isentropic compression
(
k
) 1
−
P
⎛
⎞
P
k
P
P
2
⎛
⎞
⎜ ⎜
⎟ ⎟
=
2
T
T
r
r
⎜ ⎜
⎟ ⎟
=
P
2
1
2
1
⎝
⎠
P
1
⎝
⎠
1
2-3
const. P heat addition
q
C
(
T
T
)
q
h
h
=
−
=
−
in
3
2
in
p
3
2
3-4
isentropic expansion
(
k
) 1
−
P
⎛
⎞
P
k
4
P
P
⎛
⎞
⎜ ⎜
⎟ ⎟
=
T
T
4
r
r
⎜ ⎜
⎟ ⎟
=
P
4
3
4
3
⎝
⎠
P
3
⎝
⎠
3
4-1
const. P heat rejection
q
h
h
q
Cp
(
T
T
)
=
−
=
−
out
4
1
out
4
1
q
P
P
1 (
k
)
−
1
r
out
= 1
η
=
−
k
r
2
3
r
η
−
=
=
brayton
p
brayton
P
p
q
P
P
in
1
4
h
h
h
h
T
T
T
T
−
−
−
−
2
s
1
3
4
a
2
s
1
3
4
a
η
η
η
η
=
=
=
=
1
2
3
4
1
2
3
4
−
−
−
−
h
h
h
h
T
T
T
T
−
−
−
−
2
a
1
3
4
s
2
a
1
3
4
s
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