megaset for thermo chapter 4

Boundary work definition

PdV area under the curve on a P-V diagram

Boundary work general formula

W_b = ∫ P dV

Constant pressure work

W_b = P (V2 − V1)

Constant pressure specific work

W_b = m P (v2 − v1)

Definition of specific volume

v = V/m

Volume from specific volume

V = m v

Isothermal process condition

T = constant

Isothermal ideal gas relation

PV = constant

Isothermal work

W_b = P1 V1 ln(V2/V1)

Polytropic relation

PV^n = C

Polytropic work formula

W_b = (P2 V2 − P1 V1) / (1 − n)

Polytropic pressure relation

P2 = P1 (V1/V2)^n

Rigid tank boundary work

W_b = 0

Constant volume energy relation

ΔU = m Cv (T2 − T1)

Constant pressure energy relation

ΔH = m Cp (T2 − T1)

Enthalpy definition

H = U + P V

Constant pressure identity

ΔH = ΔU + W_b

First Law closed system

Q − W = ΔU + ΔKE + ΔPE

First Law with negligible KE and PE

Q − W = ΔU

Boundary work sign convention

Expansion work is positive

Compression work sign

Work is negative

Heat sign convention

Heat added to system is positive

Ideal gas law

PV = mRT

Specific ideal gas law

Pv = RT

Mass from ideal gas law

m = PV/(RT)

Gas constant relation

R = Cp − Cv

Monatomic ideal gas Cv

Cv = (3/2) R

Monatomic ideal gas Cp

Cp = (5/2) R

Specific heat ratio

k = Cp/Cv

Boundary work on linear P-V curve

W_b = (P1 + P2)/2 * (V2 − V1)

Constant pressure condition

P remains same during the process

Piston constant pressure requirement

External pressure unchanged

Piston with stops behavior

Process becomes constant volume until stops lift

Constant volume process

No boundary work and ΔU = Q − W_sh

Stationary closed system

ΔKE = 0 and ΔPE = 0

Electrical work

W_e = V I t

Shaft work

W_sh = ∫ T dθ

Rigid insulated tank energy balance

ΔU = W_sh

Insulated system

Q = 0

Ideal gas internal energy

Depends only on temperature

Ideal gas enthalpy

Depends only on temperature

Steam tables purpose

Find u, h, v for real substances

Saturated mixture quality

x = (v − vf)/(vg − v_f)

Saturated internal energy

u = uf + x(ug − u_f)

Saturated enthalpy

h = hf + x(hg − h_f)

Saturated volume

v = vf + x(vg − v_f)

Properties needed for superheated region

P and T

Steam table superheated states

Use given P and T to read v, u, h directly

Steam table saturated states

Use T or P to find vf, vg, uf, ug, hf, hg

Critical point importance

Distinguishes superheated vs compressed regions

Phase determination using v

Compare v with vf and vg

Phase determination using T and P

Use saturation relations

kPa to kJ conversion

1 kPa·m³ = 1 kJ

Pressure-volume work unit consistency

P in kPa and V in m³ give kJ

Superheated v trend

Increases strongly with temperature

When enthalpy is preferred

Constant pressure processes

When internal energy is preferred

Constant volume processes

When ΔH equals heat transfer

Perfect gas constant pressure process

When ΔU equals heat transfer

Perfect gas constant volume process

Expansion definition

System volume increases

Compression definition

System volume decreases

Boundary work physical meaning

Work done by system pushing boundary

Internal energy physical meaning

Molecular-level energy content

Enthalpy physical meaning

Energy including flow work

Flow work definition

PV term in enthalpy

Adiabatic boundary condition

Q = 0

Quasi-equilibrium meaning

Process moves through equilibrium states

Reversible work characteristic

Max possible boundary work

Area under isothermal curve

ln-shaped area

Area under constant pressure curve

Rectangle on P-V diagram

Area under polytropic curve

Depends on n curvature

n = 0 polytropic case

Constant pressure

n = 1 polytropic case

Isothermal ideal gas

n = k polytropic case

Approximate isentropic for ideal gas

Shaft work vs boundary work

Shaft is mechanical rotational work, boundary is PdV work

Electrical vs thermal energy input

Electrical work contributes to internal energy like heat does

Internal energy change for ideal gas

ΔU = m Cv ΔT

Enthalpy change for ideal gas

ΔH = m Cp ΔT

Constant temperature internal energy change

ΔU = 0 (ideal gas)

Constant temperature enthalpy change

ΔH = 0 (ideal gas)

Conditions for ideal gas validity

High T, low P relative to critical point

Conditions for steam table use

Real water/steam not behaving like ideal gas

Maker for constant V process

Piston fixed or rigid tank

Maker for constant P process

Piston free to move with constant external force

Maker for multi-step process

Piston hits stops requiring piecewise analysis

State postulate

for simple compressible system 2 independent properties define a state

Process vs state

States are points; process is the path between them

Closed system definition

No mass crosses boundary

Control mass definition

Same mass throughout process

Energy stored as internal energy

Related to temperature for ideal gas

Work stored?

Work cannot be stored; it is path-dependent

Heat stored?

Heat cannot be stored; it is path-dependent

Compressed liquid region

T < Tsat at given P or v < v_f

Superheated region

T > Tsat or v > v_g

Saturated mixture region

vf < v < vg

Superheated properties

Always larger than saturated vapor values

How to find boundary work for tabulated data

Approximate ∫ P dV using shapes

Temperature in Kelvin

T(K) = T(°C) + 273

Pressure units conversion

1 bar = 100 kPa