A beam used in construction is made of steel, which has a coefficient of linear

Question

A beam used in construction is made of steel, which has a coefficient of linear expansion of 1.3 × 10-5 K-1. The beam is 25 m long at a temperature of 1630 K when it is made. As it cools, the temperature of the beam decreases to 295 K.

1.

What is the change in the length of the beam due to cooling?

2.

If the mass of the steel beam is 325 kg and the specific heat capacity of steel is 490 J/kg-K, how much energy did the steel beam lose due to cooling? (Use a positive value for the amount of energy.)

Explanation / Answer

(a)
dL = k×L×dt
dL = 1.3×10-/K × 25m × (1,630-295)K = .43387 meters
(b) Q (heat) = Cp (specific heat) × mass × dt (temp change)
Q = .49 kJ/kgK × 325kg × (1,630-295)K = 212,598.7 kJ

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