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GATE CH study materials
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GATE CH: Process Calculations and Thermodynamics

GATE CH · Work through your exam, one topic at a time.

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Process Calculations and Thermodynamics

This domain merges stoichiometric bookkeeping (balances with recycle, bypass and purge) with classical chemical thermodynamics (first and second laws, equations of state, phase and reaction equilibrium). The questions are numerical and reward a cleanly chosen basis.

Core rules

  • Degrees of freedom. Gibbs phase rule F = C − P + 2; the process version counts unknowns against independent balances plus specifications.
  • Recycle. Do the overall balance first, then the balance around the reactor including the recycle stream. Once-through conversion always exceeds overall conversion when a loop exists.
  • Conversion, selectivity, yield. Conversion is defined on the limiting reactant; selectivity compares desired with undesired product formed; yield is product per reactant fed.
  • First law. Steady flow: Q − W = ΔH + ΔKE + ΔPE, with W positive when done by the system.
  • Real gases. Z = PV/RT; use the virial or a cubic EOS (van der Waals, SRK, Peng–Robinson), and corresponding states with the acentric factor ω.
  • VLE. Raoult's law for ideal mixtures, modified Raoult (yP = γxP^sat) for non-ideal, Henry's law for a dilute dissolved gas.
  • Equilibrium. ln K = −ΔG°/RT and van't Hoff: d(ln K)/dT = ΔH°/RT².

Worked example

Fresh feed of 100 mol/h pure A enters a loop where A → B, per-pass conversion is 50%, overall conversion is 90%, and there is no purge. Overall balance: 90 mol/h B leaves with 10 mol/h A. Let R be recycled A. Reactor inlet is 100 + R, so 0.5(100 + R) reacts and the reactor outlet A is also 0.5(100 + R). That outlet splits into 10 leaving plus R recycled: 0.5(100 + R) = 10 + R, giving 40 = 0.5R and R = 80 mol/h. Check: inlet 180, 90 reacts (50%), outlet 90 = 80 recycle + 10 product.

Traps

  • Writing the reactor balance before the overall balance, which makes the algebra circular.
  • Mixing mass and molar bases when conversion is molar.
  • Forgetting that adding inert gas at constant pressure pushes equilibrium toward the side with more gas moles.
  • Sign errors in the first law, especially for compressors.