A steel rod is 3000 cm in diameter at 320 C A brass ring has

A steel rod is 3.000 cm in diameter at 32.0 °C. A brass ring has an interior diameter of 2.992 cm at 32.0 °C. At what common temperature will the ring just slide onto the rod? The coefficients of linear expansion of steel and brass are 1.100×10-5 , 1.900×10-5 /°C, respectively, answer in °C.

Solution

When we heat any material the distance between any point increase with same rate.

In case when the ring will just slide onto the rod, both will have equal diameter.

Final diameter of rod = d_r = d_r_0 + alpha*d_r_0*delta_T = 3+1.1*10^-5*3*(T-32)

Final diameter of ring = d_0+alpha*d_0*delta_T = 2.992+1.9*10^-5*2.992*(T-32)

Since these two are equal then,

3+1.1*10^-5*3*(T-32) = 2.992+1.9*10^-5*2.992*(T-32)

0.008 = 2.3848*10^-5*(T-32)

T = 32+335.4579 = 367.4579 degree C.