Answer:
T₂ = 18.65 °C (For Steel)
The temperature of steel first becomes 12 MPa at a temperature of 18.65°C
Explanation:
The formula for stress due to temperature difference in a member is given as follows:
Stress = αEΔT
where,
Stress = 12 MPa = 12 x 10⁶ Pa
α = co-efficient of linear expansion of the material
E = Young's Modulus of the Material
ΔT = Temperature Difference = Final Temperature - Initial Temperature
12 x 10⁶ Pa = αE(T₂ - 15°C)
FOR MAGNESIUM:
α = 25.2 x 10⁻⁶ /°C
E = 45 x 10⁹ Pa
Therefore,
12 x 10⁶ Pa = (25.2 x 10⁻⁶/°C)(45 x 10⁹ Pa)(T₂ - 15°C)
T₂ - 15°C = (12 x 10⁶ Pa)/(1.134 x 10⁶ Pa/°C)
T₂ = 15°C + 10.58°C
T₂ = 25.58 °C (For Magnesium)
FOR STEEL:
α = 17.3 x 10⁻⁶ /°C
E = 190 x 10⁹ Pa
Therefore,
12 x 10⁶ Pa = (17.3 x 10⁻⁶/°C)(190 x 10⁹ Pa)(T₂ - 15°C)
T₂ - 15°C = (12 x 10⁶ Pa)/(3.287 x 10⁶ Pa/°C)
T₂ = 15°C + 3.65°C
T₂ = 18.65 °C (For Steel)
The temperature of steel first becomes 12 MPa at a temperature of 18.65°C
