# Temperture And Kinetic Theory

1. Dec 4, 2009

### davidkis

1. The problem statement, all variables and given/known data
A brass plug is to be placed in a ring made of iron. At room temperature (20°C), the diameter of the plug is 8.764 cm and that of the inside of the ring is 8.754 cm. They must both be brought to what common temperature in order to fit?

2. Relevant equations
Change in V=B*V0*Change in T
B for brass = 56x10^-6
B for Iron = 35 x 10^-6

3. The attempt at a solution
I had no idea how to start i notice that the change in the coefficent of expansion is going to change the items dimensions but i honestly dont know where to begin, do i combine the 2 seperate formulas? how would i solve for the temperture?

2. Dec 4, 2009

### rl.bhat

Here you need not consider the volume expansion. Brass plug will pass through iron ring if their radii are the same.
Rb = Rb0( 1 + αb*Δt)
Ri = Ri0( 1 + αi*Δt)
where α is the coefficient of linear expansion which is equal to B/3.
Equate Rb and Ri and solve for Δt