ENGRD 2210

What is the ideal gas EOS?

Pv=RT

What are cp and cv?

cv: heat added at constant volume → Δu

cp: heat added at constant pressure → Δh Relation: cp−cv=R

How do you compute Δu and Δh?

Δu=∫cv​(T)dTΔh=∫cp(T)dT\Delta h = \int c_p(T) dTΔh=∫cp​(T)dT

What assumption defines incompressible behavior?

Density is constant; v = constant

Formula for enthalpy change of Incompressible substance?

h2​−h1​=c(T2​−T1​)+v(P2​−P1​)

Difference between control mass and control volume

Control mass → fixed mass, moving boundary

Control volume → fixed region in space, mass crosses boundary

What is flow work?

Work needed to push fluid into/out of control volume.Included in h = u + Pv.

What does a nozzle do?

Converts enthalpy → kinetic energy.

What does a diffuser do?

Converts kinetic energy → enthalpy (pressure rises).

What is throttling?

A constant enthalpy (h2 = h1) process. Huge irreversibility.

What does Clausius Inequality state

integral partial Q/T less than equal to zero , Q cannot flow from cold to hot without work

Entropy as a State Property

Depends only on state, not path.

Entropy Change for a System

ds = δQ_rev/T.

Entropy Balance

ΔS_system = ∫ δQ/T + S_gen.

Ideal Gas Entropy Change (T-P)

Δs = cp ln(T2/T1) − R ln(P2/P1).

Ideal Gas Entropy Change (T-v)

Δs = cv ln(T2/T1) + R ln(v2/v1).

Isentropic Process

s2 = s1; reversible and adiabatic.

Gibbs Relation (T ds)

T ds = du + P dv.

Gibbs Relation (T ds, h form)

T ds = dh − v dP.

PV Diagram Meaning

Area under curve = boundary work.

TS Diagram Meaning

Area under curve = heat transfer (internally reversible).

Isentropic Line Appearance

Vertical on T-s diagram.

Isothermal Line Appearance

Horizontal on T-s diagram.

Four Basic Steps of Rankine Cycle

Pump → Boiler → Turbine → Condenser.

Boiler Process

Liquid → superheated vapor at constant pressure.

Condenser Process

Vapor → saturated liquid at constant pressure.

Where Most Entropy Generated in Rankine Cycle

In real turbine and pump.

Brayton Cycle Steps

Compressor → Combustor → Turbine → Heat rejection.

Brayton Cycle Ideal Assumptions

Isentropic compression and expansion; constant-pressure heating/cooling.

Back Work Ratio for Brayton Cycle

Compressor work / turbine work.

Regenerator Purpose in Brayton Cycle

Improves efficiency by transferring turbine exhaust heat to compressor outlet.

Refrigeration Cycle Key Steps

Expansion → Evaporation → Compression → Condensation.

Ideal Vapor-Compression Assumptions

Isentropic compression and isenthalpic expansion.

Otto Cycle

Spark-ignition engine model.

Diesel Cycle

Compression-ignition model with constant-pressure heat addition.

Isentropic vs. Isothermal

Isentropic = constant entropy (𝑠 = const).Isothermal = constant temperature (𝑇 = const).Common Mistake: assuming constant T → constant s (not true unless reversible + ideal gas + specific conditions).

ΔU in steady flow

ΔU = 0 only if inlet and outlet temperatures are equal. Common Mistake: applying ΔU = 0 just because it's a steady-state device.

Gauge vs absolute pressure

Ideal gas law requires absolute pressure.Mistake: Using Pg instead of Pabs = Pg + Patm.

Is throttling isentropic?

No — throttling is isenthalpic (h₁ = h₂).Mistake: setting s₁ = s₂ automatically (only approximately true in ideal-gas Joule-Thomson problems).

System vs Universe entropy

ΔSsystem may be negative, but ΔSuniverse must be ≥ 0.Mistake: thinking a negative ΔSsystem makes a process impossible.

Negative entropy generation?

Never allowed — 𝑆gen ≥ 0 always.Zero only for reversible processes.Mistake: setting 𝑆gen negative to "fix the math."

When the compressed-liquid approximation is valid

If P << critical pressure and T far from saturation → use saturated liquid value at same T.

How to calculate Δh for ideal gas

Use cp(T) or constant-cp approx → Δh = cp ΔT.

How to calculate Δu for ideal gas

Use tabulated cv(T) or constant-cv approx → Δu = cv ΔT.

How to calculate entropy change for ideal gas (P-T form)

Δs = cp ln(T2/T1) − R ln(P2/P1).

How to calculate entropy change for ideal gas (v-T form)

Δs = cv ln(T2/T1) + R ln(v2/v1).

How to compute mass flow rate from velocity

ṁ = ρ A V.

How to solve turbine problems

Find h_in, h_out → Ẇ = ṁ(h_in − h_out) (neglect KE/PE).

How to solve compressor problems

Find h_out, h_in → Ẇ = ṁ(h_out − h_in).

Pump work approximation

Ẇ ≈ ṁ v (P_out − P_in).

How to compute boundary work from PV diagram

Area under process curve.

How to compute heat transfer from TS diagram

Area under curve (reversible only).

Throttling shortcut in refrigeration cycles

h3 = h4.