Wednesday, April 22, 2026

 

 

I recently saw video on the discussion on Conventional Combustion Engine Car vs Electric CarI (EV). The commentator reports that an Electric Car uses heavy and bulky Batteries. 

Heaviness uses more energy to make a car moving than a Combustion Engine Car (the engine itself is lighter and smaller than the batteries used in an EV.

Bulky means that the size of the total batteries is big and therefore the surface-area:volume ratio (SA:V) 

Surface Area / Volume

is small. This means the the eat transfer from the batteries to the surrounding area is naturally limited

The commentator the explains the difference between a small ball and big ball. Intuitively, a small ball has a small surface so heat transfer is limited. A bigger ball has a big surface and heat transfer is better. But this is completely wrong. The graph below shoes a dramtic change as the radius becomes smaller and smaller.

Wiki

For solid spheres

Plot of the surface-area:volume ratio (SA:V) for a 3-dimensional ball, showing the ratio declining inversely as the radius of the ball increases.

A solid sphere or ball is a three-dimensional object, being the solid figure bounded by a sphere. (In geometry, the term sphere properly refers only to the surface, so a sphere thus lacks volume in this context.)

For an ordinary three-dimensional ball, the SA:V can be calculated using the standard equations for the surface and volume, which are, respectively, {\displaystyle SA=4\pi {r^{2}}} and {\displaystyle V=(4/3)\pi {r^{3}}}. For the unit case in which r = 1 the SA:V is thus 3. For the general case, SA:V equals 3/r, in an inverse relationship with the radius - if the radius is doubled, the SA:V halves (see figure).

The commentator says

{\displaystyle SA=4\pi {r^{2}}} and {\displaystyle V=(4/3)\pi {r^{3}}}

are the secondary school math. 

But to get these you need high school math - integration.


sptt