A brass ring of diameter 10.00 cm at 19.0°C is heated and slipped over an aluminum rod with a diameter of 10.01 cm at 19.0°C. Assuming the average coefficients of linear expansion are constant. What if the aluminum rod were 10.02 cm in diameter?

the final temperature is

Explanation:

The change in length of a bar can be expressed with the relation;

  ---- (1)

Also ; the relative or fractional increase in length  is proportional to the change in temperature.

Mathematically;

ΔL/L_i ∝ kΔT

where;

k is replaced with ∝ (the proportionality constant )

   ---- (2)

From (1) ;

 ---  (3)

from (2)

 ---- (4)

replacing (4) into (3);we have;

On re-arrangement; we have

from the given question; we can say that :

So;

Making the change in temperature the subject of the formula; we have:

where;

= 10.02 cm

= 10.00 cm

= 19 × 10⁻⁶ °C ⁻¹

= 24  × 10⁻⁶ °C ⁻¹

= −396.1965135 ° C

≅ −396.20  °C

Given that the initial temperature

Then ;

Thus;

Thus; the final temperature is

r=rho l/a where a is the area, l is the length and rho is resistivity so the greater the area the lesser the resistance thats why the earth pin is thicker bcos current follow the shortest path, so less resistive .

the answer is false. this is because for ice to melt, it requires latent heat of melting. latent heat means heat energy required to change phase without any increase in temperatures. therefore, the ice will take energy from the environment to melt hence atmospheric temperatures will reduce.