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## Homework Statement

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

## Homework Equations

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 γ

_{iron}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 γ

_{iron}in K

^{-1}to (°C)

^{-1}?