ICAR AIEEA PG Dairy Technology 09 July 2023 (Shift 1) Paper

Materials for severe erosion and cavitation in homogenizer components:

• Standard austenitic stainless steel (AISI 304/316) is too soft to withstand intense cavitation, high-velocity liquid erosion ($100\text{--}200\text{ m/s}$), and particle impact at $200\text{--}250\text{ bar}$.
• High carbon steel lacks necessary corrosion resistance in food-contact acid/cleaning environments.
• Stellite (a non-ferrous cobalt-chromium-tungsten superalloy) or tungsten carbide is standardly used for fabricating homogenizer valves, valve seats, and impact rings due to its exceptional resistance to abrasive wear, erosion, and cavitation fatigue.
• Nichrome steel is an electrical resistance heating alloy, not a wear-resistant structural alloy.

Creep flow dynamics and Stokes' settling/creaming velocity:

• Balancing buoyancy force and hydrodynamic Stokes drag ($F_d = 3\pi \mu D_p v_t$) for a spherical droplet of diameter $D_p$ yields: $v_t = \frac{g D_p^2 (\rho_p - \rho)}{18 \mu}$ (or with fat density lighter than skim serum, creaming upward with velocity proportional to density difference $(\rho - \rho_p)$).
• The denominator $24\mu$ corresponds to drag coefficient formulations ($C_D = 24/Re$), not the integrated terminal velocity expression where the factor is 18.
• Using particle radius $R_p$ with denominator $18\mu$ is incorrect; the radius formulation requires a denominator of $9\mu$ ($v_t = \frac{2 g R_p^2 \Delta\rho}{9 \mu}$).
• Using linear radius $R_p$ violates dimensional homogeneity (velocity must depend quadratically on particle size).

Classification of idealized thermodynamic gas power cycles:

• Dual cycle supplies heat partly at constant volume and partly at constant pressure, and rejects heat at constant volume.
• Otto cycle supplies heat at constant volume and rejects heat at constant volume.
• The Atkinson cycle (invented by James Atkinson in 1882) is an ideal thermodynamic cycle where heat addition occurs at constant volume, expansion continues down to atmospheric pressure (longer expansion stroke than compression stroke), and heat rejection takes place at constant pressure.
• Diesel cycle supplies heat at constant pressure and rejects heat at constant volume.

Thermodynamic efficiency of reversible Carnot heat engines:

• $\frac{T_1}{T_1 - T_2}$ represents the coefficient of performance (COP) of a Carnot heat pump, not engine efficiency.
• The thermal efficiency $\eta$ of a reversible Carnot heat engine operating between source temperature $T_1$ (higher temperature) and sink temperature $T_2$ (lower temperature) is given by: $\eta = \frac{W}{Q_1} = \frac{Q_1 - Q_2}{Q_1} = \frac{T_1 - T_2}{T_1} = 1 - \frac{T_2}{T_1}$.
• $\frac{T_2(T_1 - T_2)}{T_1(T_1 - T_2)}$ reduces algebraically to $T_2/T_1$, which is the fraction of heat rejected, not efficiency.
• $\frac{T_1 T_2}{T_1 - T_2}$ is dimensionally incorrect.

State functions and thermodynamic properties of ideal gases:

• Pressure alone does not dictate internal energy; at constant temperature, isothermal pressure changes cause zero change in ideal gas internal energy.
• Volume alone does not dictate internal energy; free expansion into vacuum produces no change in temperature or internal energy.
• According to Joule's law of ideal gases, the internal energy $U$ of an ideal gas depends solely and exclusively on its absolute temperature: $U = f(T)$, with $dU = m c_v dT$. Since intermolecular attractive forces are negligible in ideal gas models, changing volume or pressure without changing temperature does not alter molecular kinetic energy.
• For real gases, $U$ depends on $T$ and $v$, but for an ideal gas it is strictly a function of absolute temperature alone.