UNIT-1
Thermodynamics
Important formula
1. Absolute pressure = Atmosphere pressure ± Gauge pressure
2. Absolute temperature = tº + 273
3. Heat transfer Q = m.c (T2-T1)
4. Ratio of specific heat γ = Cp / Cv
5. Power = work done / time in seconds KJ/sec (or) KW
6. Potential energy P.E = mgz joules
7. Kinetic energy K.E = ½ mv2 joules
8. Flow energy F.E = PV N.M (or) Joules
9. Internal Energy U = mcv dt KJ
10. Change in internal energy ΔU = mcv (T2 – T1)
11. External energy W = P.dv
IMORTENT VALUES
1. Atmosphere pressure = 760mm of mercury
= 1.01325 bar
= 101.325 KN/m2 (or) kpa
= 10.1325 N/ m2 (or) pa
2. Standard temperature = 15ºC
3. Standard pressure = 101.325 KN/m2
4. Normal temperature = oº C
5. For Air Cp = 1.005 KJ/kg.k
6. Cv = 0.718 KJ/kg.k
7. For water Cp = 4.19 KJ/kg.k
8. 1KW – hr = 3600 KJ




Thermodynamic Process of Perfect Gases

IMPORTANT VALUES
1. Gas constant R = 0.287 KJ/kg.k
2. Specific heat at constant pressure for air Cp = 1.005 KJ/kg.k
3. Specific heat at constant volume for air Cv = 0.718 KJ/kg.k
4. At N.T.P conditions Vmole = 22.4 m3 / kg – mole
5. Universal gas constant Ru = 8314 J/kg - mole k

Important formula
1. Constant (when T is Constant) = P1 V1 = P2 V2 = P3 V3
2. Constant (when V is Constant) = P1/T1 = P2/T2 = P3/T3
3. Characteristic gas constant = PV= MRT
4. Constant from gas equation = P1 V1/T1 = P2 V2/T2 = P3 V3/T3
5. Cp – Cv = R
6. Cv = R/γ-1
7. Cp/Cv = γ
8. Weight = mass × acceleration due to gravity
9. Density ρ = Mass / Volume kg/m3
10. Specific weight W = Weight / Volume (or) ρg N/m3
11. Specific gravity S = Density of the substance / Density of the standard substance
12. Pressure P = Force / Area
13. Density of water = 1000kg /m3






CHANGE IN ENTROPY mcv log In [T2 ̶ T1]
(or)
mcv log In [P2/P1]
mcp log In [T2 ̶ T1]
(or)
mcp log In [V2/V1]
mR log In [V2 ̶ V1]
(or)
mR log In [P1/P2]
0 Refer Polytrophic Process
CHANGE IN ENTHALPHY
(ΔH) J 0r KJ
mcp (T2 ̶ T1) mcp (T2 ̶ T1) 0 mcp (T2 ̶ T1) mcp (T2 ̶ T1)
HEAT SUPLLIED (Q) J or KJ mcv (T2 ̶ T1) mcp (T2 ̶ T1) P1 V1 log In [V2/ V1]
(or)
MRT log In [V2/ V1]
0 P1V1 ̶ P2V2/n – 1 + mcv (T2 ̶ T1) (or)
γ- n /γ – 1 × MR[T1 ̶ T2]/ n – 1
CHANGE IN INTERNAL ENERGY (ΔU) J or KJ mcv (T2 ̶ T1) mcv (T2 ̶ T1) 0 mcv (T2 ̶ T1) mcv (T2 ̶ T1)
WORK DONE (W) Nm or KNm 0 P[V2 ̶ V1] (or) MR (T2 ̶ T1) P1 V1 log In [V2/ V1]
(or)
MRT log In [V2/ V1]
P1V1 ̶ P2V2/γ – 1 (or)
MR[T1 ̶ T2]/ γ – 1
P1V1 ̶ P2V2/n – 1 (or)
MR[T1 ̶ T2]/ n – 1
P.V.T RELATION P1/T1 = P2/T2 V1/T1 = V2/T2 P1 V1 = P2 V2 P1 V1 γ = P2 V2 γ T1/T2=[ V1/V2]γ-1 T1/T2=[P1/P2]γ-1/γ P1 V1 n = P2 V2 n T1/T2=[ V1/V2]n-1 T1/T2=[P1/P2]n -1/n
TYPES OF REVESIBLE NON-FLOW PROCESS Constant volume (or) Isochoric (V=Constant) Constant Pressure (or) Isobaric (P=Constant) Constant Temperature (or) Isothermal (or) Hyperbolic (T=Constant) Adiabatic Process (or) Isentroph (PVγ=Constant) General expansion (or) Polytrophic (PVn=Constant)
S.NO 1 2 3 4 5

UNIT-2
Thermodynamic Air cycles, steady flow
Energy equation
Important formula

CARNOT CYCLE
1.ɳcarnot = T2 – T1 / T2
2. Thermal efficiency = 1-[T1/T2]
3. Heat supplied ɳcarnot = Work / Heat
4. Heat (Q) = Work / ɳcarnot
5. Ratio of adiabatic expansion (r) = [T1/T2]1/γ-1
OTTO CYCLE
1. Adiabatic compression ɳOtto = 1- [1/rγ – 1]
2. r = [T1/T2]1/γ-1 (or) Vc+Vs/ Vc
3. Initial efficiency ɳ1 = 1- [1/r1 γ – 1]
ɳ2 = 1- [1/r2 γ – 1]
4. Increase efficiency = ɳ2 - ɳ1
5. Stroke Volume Vs = π/4×d2×L
6. ɳActual = ɳrel = ɳOtto
7. ɳrel = Thermal efficiency (Actual) / ɳOtto (Air standard efficiency)
8. Work done Qs = mcv [T3 – T2]
9. Qr = mcv [T4 – T1]
10. γ = Cp/Cv
DIESEL CYCLE
1. ɳ Diesel = 1- [1/γ× rγ-1] × [ργ – 1/ρ – 1]
2. Cut off Ratio ρ = Compression Ratio/ Expansion Ratio


Steady Flow energy equation
Important formula
1. Steady flow energy equation(SFEE) = gZ1+c12/2+u1+p1v1+Q = gZ2+c22/2+u2+p2v2+W (or)
gZ1+c12/2+u1+h1+Q = gZ2+c22/2+u2+h2+W (h1, Q, h2, we are in J/kg)
2.SFEE For
1. Steam boiler Q = h2 – h1 J/kg or KJ/kg
2. Steam condenser Q = h2 – h1 J/kg or KJ/kg
3. Steam Nozzle c22/2 – c12/2 = h2 – h1 J/kg (h1, h2, W are in J/kg)
[IMG]file:///C:/Users/SUDHAR~1/AppData/Local/Temp/msohtmlclip1/01/clip_image001.gif[/IMG][IMG]file:///C:/Users/SUDHAR~1/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif[/IMG] C22 – c12/2×1000 = h2 – h1 KJ/kg (h1, h2, W are in KJ/kg)
[IMG]file:///C:/Users/SUDHAR~1/AppData/Local/Temp/msohtmlclip1/01/clip_image003.gif[/IMG][IMG]file:///C:/Users/SUDHAR~1/AppData/Local/Temp/msohtmlclip1/01/clip_image004.gif[/IMG] 4. Final Velocity c2 = √2×1000 × (h1 – h2) + c12 m/s (h1, h2, in KJ/kg) (or)
[IMG]file:///C:/Users/SUDHAR~1/AppData/Local/Temp/msohtmlclip1/01/clip_image005.gif[/IMG][IMG]file:///C:/Users/SUDHAR~1/AppData/Local/Temp/msohtmlclip1/01/clip_image006.gif[/IMG] C2 = √2×cp×T1×[1-(p1/p2)γ-1/γ] + c12 m/s (cp in J/kg.K)
C2 = √2×1000 × cp×T1 [1-(p1/p2)γ-1/γ] + c12 m/s (cp in KJ/kg.K)
5. Rotary air compressor W = h1 – h2 J/kg
6. Reciprocating air compressor W = Q + (h1 – h2) J/kg
7. Steam and gas turbine W = h1 – h2 J/kg
8. Non flow energy equation Q = W + ΔU J/kg