GATE CH flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Overall material balance

For a steady-state unit with no reaction, total mass in equals total mass out. With reaction, use component balances with generation terms; C independent component balances exist for C species.

Recycle ratio

Ratio of recycled stream flow to fresh feed flow. It changes the reactor inlet concentration and per-pass conversion but not the overall conversion for a fixed separator performance.

Kirchhoff's law

Relates heat of reaction at one temperature to another: ΔH_r(T2) = ΔH_r(T1) + ∫(T1 to T2) ΔC_p dT, where ΔC_p is the product-minus-reactant heat capacity difference.

Adiabatic temperature rise

Maximum temperature increase in an adiabatic reactor at full conversion: ΔT_ad = (−ΔH_r)·X/(Σ Θ_i C_p,i). It sets the vertical span of the operating line on a T-versus-conversion plot.

Relative volatility

α_ij = (y_i/x_i)/(y_j/x_j), equal to P_i^sat/P_j^sat for ideal Raoult's law systems. Values near 1 mean difficult separation; α below 1 means component i is heavier.

Log-mean temperature difference

ΔT_lm = (ΔT1 − ΔT2)/ln(ΔT1/ΔT2) for countercurrent or cocurrent exchangers. Use it with Q = UAΔT_lm and a correction factor F for multipass shell-and-tube units.

CSTR versus PFR volume

For first-order kinetics at equal conversion and feed rate, V_CSTR = vX/[k(1−X)] and V_PFR = (v/k)ln[1/(1−X)]. The CSTR is always larger because it operates at the low outlet concentration.

Ergun equation

Predicts pressure drop through a packed bed as the sum of viscous (150μu(1−ε)²/(ε³d_p²)) and inertial (1.75ρu²(1−ε)/(ε³d_p)) terms per unit bed length.

Hatta number

Ha = √(kD_AB)/k_c compares reaction rate to diffusion rate in a film. Large Ha means fast reaction confined near the interface; small Ha means the reaction is slow relative to diffusion.

Fenske equation

Gives minimum theoretical stages at total reflux: N_min = ln[(x_D/(1−x_D))((1−x_B)/x_B)]/ln α_avg. It assumes constant relative volatility and is used with the Gilliland correlation.

Kremser equation

Relates stage count to absorption factor S = L/(mV) in countercurrent absorption or extraction: (Y_N − Y_0)/(Y_1 − Y_0) = (S^(N+1) − S)/(S^(N+1) − 1).

Integral rate method

Tests an assumed order by plotting the integrated rate law. First order gives a straight line for −ln(1−X) versus t; second order gives a straight line for X/(1−X) versus t.

Multiple steady states

In a non-isothermal CSTR, the S-shaped heat-generation curve can intersect the linear heat-removal line at three points. The middle intersection is unstable and cannot be maintained in practice.

Azeotrope condition

At an azeotropic point the vapor and liquid compositions are equal, so y_i = x_i and relative volatility is unity. Ordinary distillation cannot cross this composition barrier.

Humidity ratio

Y = 0.622 p_w/(P − p_w) kg water per kg dry air. It is unchanged by heating or cooling without condensation and fixes the position on a psychrometric chart.

Heat and mass transfer analogy

Chilton–Colburn analogy equates Nu/Pr^(1/3) with Sh/Sc^(1/3), letting a heat transfer coefficient predict a mass transfer coefficient when the geometries and flow regimes match.

Ziegler–Nichols reaction curve

Open-loop tuning from a first-order-plus-dead-time fit: K_c = 1.2τ/(K_p θ), τ_I = 2θ, τ_D = 0.5θ. It gives aggressive settings with roughly quarter-amplitude damping.

Ultimate gain tuning

Increase proportional gain until the loop oscillates continuously; record K_cu and period P_u. PID settings are K_c = K_cu/1.7, τ_I = P_u/2, τ_D = P_u/8.

Routh–Hurwitz criterion

Builds a table from the closed-loop characteristic polynomial. The number of sign changes in the first column equals the number of right-half-plane roots, so no sign change means stability.

Decay ratio

Ratio of successive peak amplitudes in an underdamped response. A decay ratio of one quarter corresponds to a damping coefficient near 0.216 and is a common tuning target.

Control valve sizing

Liquid flow through a valve follows Q = C_v√(ΔP/G). Choked flow and cavitation limit the usable pressure drop and must be checked against the vapor pressure.

HAZOP guide words

Standard prompts applied to node parameters: NO, MORE, LESS, AS WELL AS, PART OF, REVERSE and OTHER THAN. Each deviation is examined for causes, consequences and safeguards.

Limiting oxygen concentration

The maximum oxygen level in a fuel–air–inert mixture that cannot support ignition. Inerting below the LOC, with a safety margin, prevents explosion in vessels and dryers.

Six-tenths rule

Scales equipment cost with capacity: C2 = C1(S2/S1)^0.6. The exponent ranges from about 0.4 to 0.9 depending on equipment type and should be checked for the specific item.

Lang factor

Multiplies delivered equipment cost to estimate fixed capital investment. Typical values are about 3.1 for solids processing, 4.7 for mixed, and 5.0 for fluid processing plants.

Van der Waals equation

Cubic equation of state (P + a/V_m²)(V_m − b) = RT with a = 27R²T_c²/(64P_c) and b = RT_c/(8P_c). It predicts Z_c = 0.375, overestimating the true value near 0.27.

Fugacity coefficient

φ_i = f_i/(y_i P) measures departure from ideal-gas behavior. It equals 1 for an ideal gas and is computed by integrating the equation of state over volume.

Wilson equation limitation

The Wilson activity coefficient model cannot predict liquid–liquid phase splitting. NRTL and UNIQUAC include the extra interaction parameter needed to represent partially miscible systems.

Lumped capacitance validity

Spatially uniform body temperature is assumed when the Biot number hL/k is below 0.1. Then temperature decays exponentially with time constant ρVC_p/(hA).

Dittus–Boelter correlation

Nu = 0.023 Re^0.8 Pr^n for turbulent flow in smooth tubes, with n = 0.4 for heating and 0.3 for cooling. Valid for Re above about 10,000 and moderate property variation.

View factor reciprocity

For any two surfaces, A_i F_ij = A_j F_ji. Combined with the summation rule Σ F_ij = 1 for an enclosure, it lets unknown view factors be found from known geometry.

Van 't Hoff equation

d(ln K)/dT = ΔH°/(RT²). An endothermic reaction has K increasing with temperature; an exothermic one has K decreasing. Integrating assumes constant ΔH° over the range.