Respuesta :
Answer:
The temperature of steel first becomes 12 MPa at a temperature of 18.65°C
Explanation:
Given that,
Diameter = 50 mm
Temperature = 15°C
Diameter = 10 mm
Stress = 12 MPa
We need to calculate the temperature of steel
Using formula of stress
[tex]stress=\alpha Y\Delta T[/tex]
Where, Y = young modulus
T = temperature
[tex]\alpha[/tex]= coefficient of linear expansion of the material
Put the value into the formula
[tex]12\times10^{6}=17.3\times10^{-6}\times190\times10^{9}\times(T_{2}-15)[/tex]
[tex](T_{2}-15)=\dfrac{12\times10^{6}}{17.3\times10^{-6}\times190\times10^{9}}[/tex]
[tex]T_{2}=3.650+15[/tex]
[tex]T_{2}=18.65^{\circ}[/tex]
We need to calculate the temperature of magnesium
Using formula of stress
[tex]stress=\alpha Y\Delta T[/tex]
Put the value into the formula
[tex]12\times10^{6}=25.2\times10^{-6}\times45\times10^{9}\times(T_{2}-15)[/tex]
[tex](T_{2}-15)=\dfrac{12\times10^{6}}{25.2\times10^{-6}\times45\times10^{9}}[/tex]
[tex]T_{2}=10.5+15[/tex]
[tex]T_{2}=25.58^{\circ}[/tex]
Hence, The temperature of steel first becomes 12 MPa at a temperature of 18.65°C
