An iron ring of radius 2.1 m is to be fitted on the rim of a wheel of radius 2.121 m. The coefficient of volume expansion for iron is 3.6 x 10-5 K-1. By how much should the temperature of the ring be increased?
(a) 532 °C
(b) 833 °C
(c) 278 °C
(d) 378 °C
ΔV/V = γΔθ
where ΔV in the change in volume on expansion, V is the original volume, γ is the coefficient of volume expansion & Δθ is the rise in temperature.
3. The attempt at a solution
Well, obviously, ΔV = 0.021 m. Now, if I use the value of γiron in (°C)-1, that is, 12 x 10-6 (not given in the problem), I get the correct answer of 833 °C. However, if I use the given value of 3.6 x 10-5 K-1, I get the answer as 277.78 K, which comes out to be approximately 4 °C.
Why is there a discrepancy?
How do I convert γiron in K-1 to (°C)-1?