Physics for ECE
Lesson-end Activities
1. Two bodies made of the same material have the same external dimensions and
appearance, but one is solid and the other is hollow. When their temperature is
increased, is the overall volume expansion the same or different? Why?
- Yes, the overall volume expansion will be same in both cases. Thatโs
because the bodies, being made of the same material, have the same
volume coefficient of expansion. Also, before the measurement is taken,
both objects must have come to equilibrium at the new temperature. To
further explain, the hollow one will expand the same as if it were also solid.
This is due to the molecules in which its energy increases that leads to any
two molecules of the solid to move further apart. Hence, hollow bodies
expand just like the material that surrounds them. The external
dimensions of both objects would increase the same amount.
2. Many automobile engines have cast-iron cylinders and aluminum pistons. What
kinds of problems could occur if the engine gets too hot? (The coefficient of volume
expansion of cast iron is approximately the same as that of steel.)
- With the rise in engine temperature for the iron cast and aluminum pistons,
it is expected that there would be expansion in the volume of both elements.
From the table of Coefficients of Volume Expansion in the discussion,
Aluminum has a larger thermal expansion coefficient than steel or is double
the coefficient of steel. This means that at any temperature, the diameter
of the aluminum piston will expand more than the inside diameter of the
cylinder and can cause a high heat capacity absorbed by the piston. With
this, the problems that could occur if the engine gets too hot are that the
piston will not be able to freely move inside the iron cast and it would cause
damage to engine due to the friction between the piston and the cast iron.
3. The Humber Bridge in England has the worldโs longest single span, 1410 m.
Calculate the change in length of the steel deck of the span when the temperature
increases from โ8โ ๐ก๐ 20โ.
Solution:
โ๐ = ๐ โ ๐๐
โ๐ = 20โ โ (- 8โ)
โ๐ = 28๐ถยฐ
โ๐ = 28k
โ๐ฟ = ๐ผ๐ฟ0โ๐
โ๐ฟ = (1.2ร10โ5 ๐โ1 ) (1410m) (28k)
โ๐ฟ = 0.4737m
