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#surface area

2 public questions tagged with this topic.

Fluid Pressure, Pascal's Law and Manometers

A brass cube of side 15cm at 35∘C is heated to 135∘C. What is the increase in its surface area if one face is 225cm2? (α

Given: A0 = 225cm2 (one face), total surface area = 6×225 = 1350cm2, ΔT = 135−35 = 100∘C, αl = 1.8×10−5K−1. Area expansion: ΔA = A0×2αlΔT. For total surface area: ΔA = 1350×2×1.8×10−5×100 = 1350×3.6×10−3 = 4.86cm2.

Ref: NCERT Class 11 Physics, Chapter 11: Thermal Properties – Calorimetry.

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Adaptation

Which of the following has high surface area to volume ratio?

Surface area scales approximately with the square of linear dimension, whereas volume and mass scale with the cube. Small animals therefore possess more surface area per unit body volume than large animals. Among the listed examples, a desert rodent is far smaller than a polar bear, whale, or penguin and consequently has the highest surface-area-to-volume ratio. This geometry promotes rapid exchange of heat with the environment. In a hot desert, it can assist heat dissipation when ambient conditions permit, but it also creates a risk of rapid heat gain and water loss; nocturnal activity, burrowing, concentrated urine, and reduced evaporative loss help compensate. Large whales have particularly low relative surface area and retain heat effectively in cold water, aided by blubber. Polar bears and penguins likewise combine compact bodies with insulation to limit heat loss. Shape and appendage size can modify the simple size effect, so exact comparisons require measurements, but the large difference in body size dominates here. The principle underlies Bergmann’s rule and explains why small endotherms generally need higher mass-specific metabolic rates to replace heat lost across their relatively extensive body surface.

Ref: Evolutionary Analysis, Herron & Freeman, 5th Ed., Ch. 10

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