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Question
Solve the following problem.
A blacksmith fixes iron ring on the rim of the wooden wheel of a bullock cart. The diameter of the wooden rim and the iron ring are 1.5 m and 1.47 m respectively at room temperature of 27 °C. To what temperature the iron ring should be heated so that it can fit the rim of the wheel? (αiron = 1.2 × 10–5K–1).
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Solution
Given: dw = 1.5 m, di = 1.47 m, T1 = 27 °C.
αi = 1.2 × 10–5/ K
To find: Temperature (T2)
Formula: α = `("d"_"w" - "d"_"i")/("d"_"i" ("T"_2 - "T"_1))`
Calculation: From formula,
`"T"_2 = ("d"_"w" - "d"_"i")/("d"_"i" alpha) + "T"_1`
`= (1.5 - 1.47)/(1.47 xx 1.2 xx 10^-5) + 27`
= 1700.7 + 27
= 1727.7 °C
Iron ring should be heated to temperature of 1727.7 °C.
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