Question

A building made with a steel structure is 650 m high on a winter day when the temperature is 0° F. How much taller (in cm) is the building when it is 100° F? (The linear expansion coefficient of steel is 11 10-6 (°C)-1.) 36 46 40 65 71

Answer 1

Linear coefficient of expansion of steel = $\alpha$ = 11 x 10^-6oC^-1

Temperature of on a winter day = T₁ = 0 ^oF

Converting this temperature to degrees celsius,

$T_{1} = (0 - 32)\times (\frac{5}{9})$

T₁ = -17.78 ^oC

Length of the building on the winter day = L = 650 m

New temperature = T₂ = 100 ^oF

Converting this temperature to degrees celsius,

$T_{2} = (100 - 32)\times (\frac{5}{9})$

T₂ = 37.78 ^oC

Change in the height of the building when it is 100 ^oF = $\Delta$ L

$\Delta L = L\alpha (T_{2} - T_{1})$

$\Delta L = (650)(11\ast 10^{-6})[37.78 - (-17.78)]$

$\Delta$L = 0.40 m

$\Delta$L = 40 cm

Amount the building is taller by when the temperature is 100 ^oF = 40 cm