Thermodynamics 1 Equations

Question 1

Sign Convention for Heat

Answer 1

Heat IN is +ive

Question 2

Sign Convention for Work

Answer 2

Work OUT is +ive

Question 3

Displacement Work

Answer 3

W = int P dV

Question 4

Isothermal PV relationship

Answer 4

P V = m R T

Question 5

Isentropic PV relationship

Answer 5

P V^γ = k

Question 6

First Law of Thermodynamics

Answer 6

Q - W = ΔU (for a closed system)

Question 7

Enthalpy Definition

Answer 7

h = u + P v

Question 8

Ideal Gas Law

Answer 8

P v = R T

Question 9

Specific Heat (constant volume)

Answer 9

Cv = du/dT

Question 10

Change in u

Answer 10

u2 - u1 = Cv * ( T2 - T1 )

Question 11

Specific Heat (constant pressure)

Answer 11

Cp = dh/dT

Question 12

Change in h

Answer 12

h2 - h1 = Cp * ( T2 - T1 )

Question 13

Specific Heat Relationship

Answer 13

R = Cp - Cv

Question 14

γ in terms of specific heats

Answer 14

γ = Cp / Cv

Question 15

Dryness fraction from specific volume

Answer 15

x = (v - vf) / (vg - vf)

Question 16

Dryness fraction from specific enthalpy

Answer 16

x = (h - hf) / (hg - hf)

Question 17

Dryness fraction from specific entropy

Answer 17

x = (s - sf) / (sg - sf)

Question 18

Specific enthalpy h_fg for wet steam

Answer 18

hfg = hg - hf

Question 19

Specific enthalpy h of wet steam

Answer 19

h = hf + x * hfg

Question 20

Heat (Q) and Temp (T) relationship for a reversible heat engine

Answer 20

Qh / Th = Qc / Tc

Question 21

Reversible Heat Temp relationship (condition)

Answer 21

int dQ/T = 0

Question 22

Irreversible Heat Temp relationship condition

Answer 22

int dQ/T < 0

Question 23

Entropy Definition

Answer 23

dS = dQ(rev) / T

Question 24

Change in Entropy

Answer 24

S2 - S1 = int dQ(rev)/T

Question 25

Reversible change in Entropy

Answer 25

S2 - S1 = int dQ / T

Question 26

Irreversible change in Entropy

Answer 26

S2 - S1 > int dQ / T

Question 27

1st T ds Equation

Answer 27

T ds = du + P dv

Question 28

2nd T ds Equation

Answer 28

T ds = dh - v dP

Question 29

Integrated T ds equation in T and v

Answer 29

s2 - s1 = Cv ln(T2/T1) + R ln(v2/v1)

Question 30

Integrated T ds equation in T and P

Answer 30

s2 - s1 = Cp ln(T2/T1) - R ln(P2/P1)

Question 31

Integrated T ds equation in P and v

Answer 31

s2 - s1 = Cp ln(v2/v1) + Cv ln(P2/P1)

Question 32

Isentropic T v relationship

Answer 32

T * v^(γ - 1) = k

Question 33

Isentropic T P relationship

Answer 33

T / P^((γ-1)/γ) = k

Question 34

Isentropic Efficiency (ηs) for a turbine

Answer 34

ηs = (h1 - h2) / (h1 - h2s)

Question 35

Isentropic Efficiency (ηs) for a compressor

Answer 35

ηs = (h2s - h1) / (h2 - h1)

Question 36

Reversible Heat Transfer (Q) from a T s Diagram

Answer 36

Q = int T ds

Question 37

SFEE

Steady Flow Energy Equation

Answer 37

Qdot- Wdot = mdot(h + 1/2 c^2 + gz)[out] - mdot(h + 1/2 c^2 + gz)[in]

Question 38

Heat Engine Efficiency for any engine

Answer 38

η = 1 - Qc/Qh

Question 39

Reversible Heat Engine Efficiency (Carnot Efficiency)

Answer 39

η = 1 - Tc/Th

Question 40

COP for a Refrigerator

Answer 40

COP = Qc / (Qh - Qc)

Question 41

COP for a Reversible Refrigerator

Answer 41

COP(rev) = Tc / (Th - Tc)

Question 42

COP for a Heat Pump

Answer 42

COP = Qh / (Qh - Qc)

Question 43

COP for a Reversible Heat Pump

Answer 43

COP(rev) = Th / (Th - Tc)