Question 9 of 9: Physical-Property Measurement Methods for Fruit, Fried, and Vegetable Products

Question 9: Physical-Property Measurement Methods for Fruit, Fried, and Vegetable Products (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

(a) Volume of a fruit product. (1) Liquid (water) displacement: submerge the fruit in a graduated vessel and read the volume of water displaced (Archimedes' principle); simple but only suitable for fruit that does not absorb water during the brief immersion. (2) Platform (buoyancy) method with a low-surface-tension, non-absorbing liquid (e.g. toluene): suspend the sample from an analytical balance, weigh it in air and then fully submerged, and compute volume from the buoyant weight loss and the liquid's density — avoids the wetting/absorption problems of water. (3) Gas (air) pycnometry: seal the sample in a chamber of known volume and use the pressure change on admitting a known volume of gas (Boyle's law) to back out the sample's true volume without any liquid contact at all, the preferred method when even brief contact with a liquid would alter the sample.

(b) Porosity of a fried food product. (1) Bulk/true-density method: measure the bulk (apparent, including internal pores) density geometrically or by displacement in a non-penetrating fluid, and the true (solid-material) density by gas pycnometry or by displacement in a fine, freely flowing solid (e.g. glass beads) that fills only the open pores; porosity follows from \(\varepsilon = 1-\rho_{\text{bulk}}/\rho_{\text{true}}\). (2) Gas (air) pycnometry directly: compare the apparent volume from the sample's outer dimensions/displacement with the pycnometer-measured true solid volume, giving porosity from the volume difference without a separate mass-based density calculation. (3) Image analysis of a cross-section: cut or CT-scan a cross-section, binary threshold the image into pore versus solid pixels, and take the pore area fraction as an estimate of volumetric porosity (valid if the pore structure is reasonably isotropic).

(c) Surface area of a vegetable product. (1) Geometric (dimensional) modelling: measure the key linear dimensions (length, width, thickness) and fit the product to the nearest regular solid (sphere, oblate spheroid, cylinder), computing surface area from the corresponding closed-form formula, optionally scaled by an empirical shape factor determined from a reference sample. (2) Surface replica / coating method: coat the product with a thin, uniform layer of a known-density material (e.g. melted paraffin wax) of controlled thickness, weigh the coating applied, and back-calculate the coated area from the coating's mass, density and thickness — or, equivalently, carefully peel the skin and measure its flattened area directly by planimetry or digital image analysis.

(d) Freezing-point depression for beverage solids concentration. Dissolved solids are a colligative solute, so they depress the beverage's freezing point below that of pure water by an amount proportional to the total molal concentration of dissolved species, $$\Delta T_f = K_f\, m,$$ with \(K_f = 1.86\ ^{\circ}\text{C}\cdot\text{kg/mol}\) for water. In practice, a cryoscope measures the freezing point of the beverage sample precisely (by supercooling it slightly and detecting the plateau where ice first nucleates) and compares it against a calibration curve built from standard solutions of the beverage's characteristic solute (e.g. sucrose for a fruit juice, giving a direct °Brix-equivalent readout) so that a single freezing-point measurement gives the total dissolved-solids concentration without any separate density or refractometer measurement; the same principle, applied to milk, is the standard dairy-industry test for detecting added water, since any dilution measurably raises the (less-depressed) freezing point toward 0 °C.

(e) Why a solute lowers vapour pressure. At the liquid's surface, some fraction of the sites that would otherwise be occupied by solvent molecules are instead occupied by non-volatile solute molecules, so fewer solvent molecules are available at the interface to escape into the vapour phase per unit time — the evaporation rate falls, while the rate at which vapour molecules condense back into the liquid is essentially unaffected by the solute (each returning vapour molecule still has the same chance of landing on and being captured by the liquid surface). Equilibrium vapour pressure is reached when evaporation and condensation rates match, so with evaporation suppressed and condensation unchanged, a new equilibrium is reached at a lower vapour pressure. Equivalently, in thermodynamic terms, dissolving a solute raises the entropy (disorder) of the liquid phase relative to the pure liquid, lowering the solvent's chemical potential and hence its "escaping tendency" into the vapour phase — this is the same underlying effect (Raoult's law) responsible for both freezing-point depression in part (d) and vapour-pressure lowering here.