Question

The active element of a certain laser is an ordinary glass rod 19.3 cm long and 1.15 cm in diameter. If the temperature of the rod increases by 71.9°C, calculate its increase in length. (Use 9.0×10^-6 °C^-1 for the coefficient of linear expansion for glass. Use this value to find the coefficient of volume expansion in the later parts of the problem.)

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Calculate its increase in diameter.

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Calculate its increase in volume.

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Answer 1

a) Increase in length = (coefficient of linear expansion) x ( original length) x (rise in temp.)

coefficient of linear expansion α of glass is between 9.0×10-6 °C-1
coefficient of superficial expansion is twice the above value
coefficient of cubical expansion is thrice the above value

Increase in length = 9.0×10-6 °C-1x19.3x71.9 = 0.01248 cm

b) surface area = pi d h

New area = original area ( 1 + βt )

diameter = 1.15*9*(10⁻⁶)*71.9 = 0.0007441 cm

c) similarly, increase in volume can be obtained as in case (a),

volume = π*{(1.15/2)²}*19.3*3*9*(10⁻⁶)*71.9 = 0.03891 cm³[As we know γ = 3*α]

coefficient of cubical expansion γ = 3α