Answer:
Temperature to which the shaft must be cooled, [tex]\theta_2 = -180.61 ^0C[/tex]
Explanation:
Diameter of the shaft at room temperature, d₁ = 40 mm
Room temperature, θ₁ = 21°C
Coefficient of thermal expansion, [tex]\alpha = 24.8 * 10^{-6} / ^0 C[/tex]
The shaft is reduced in size by 0.20 mm:
Δd = - 0.20 mm
The temperature to which the shaft must be cooled, θ₂ = ?
The coefficient of thermal expansion is given by the equation:
[tex]\alpha = \frac{\triangle d}{d_1 * \triangle \theta}\\\\24.8 * 10^{-6} = \frac{-0.20}{40 * \triangle \theta}\\\\\triangle \theta = \frac{-0.20 }{24.8 * 10^{-6} * 40} \\\\\triangle \theta = - 201.61 ^0 C\\\triangle \theta = \theta_2 - \theta_1\\\\- 201.61 = \theta_2 - 21\\\\\theta_2 = -201.61 + 21\\\\\theta_2 = -180.61 ^0C[/tex]
