Steel rails for a train track are laid in a region subject to extremes of temperature. The distance from one juncture to the next is 4.41 m, and the cross-sectional area of the rails is 60 cm2. If the rails touch each other without buckling at the maximum temperature, 60.0 °C, how much space will there be between the rails at -12.0 °C?
(The linear expansion coefficient of steel is 1.3·10-5 / °C)
4.41*(60-(-12))*1.3*10^(-5) 100 =0,412 CM
To find the space between the steel rails at -12.0 °C, we can use the concept of thermal expansion.
The formula for linear thermal expansion is given as:
∆L = α * L0 * ∆T
Where:
∆L is the change in length
α is the coefficient of linear expansion
L0 is the original length
∆T is the change in temperature
First, let's calculate the change in length (∆L) at the maximum temperature of 60.0 °C.
∆L = α * L0 * ∆T
∆L = (1.3 * 10^-5 / °C) * 4.41 m * 60.0 °C
∆L = 3.1398 * 10^-3 m
Next, we need to calculate the original length (L0). Since the distance between junctures is given as 4.41 m, and there are two rails, the total length of the rails is 2 * 4.41 m = 8.82 m.
Now, let's calculate the change in length (∆L) at -12.0 °C.
∆L = α * L0 * ∆T
∆L = (1.3 * 10^-5 / °C) * 8.82 m * (-12.0 °C)
∆L = -1.2756 * 10^-3 m
Since the rails touch each other without buckling at the maximum temperature, the total change in length (∆L) is distributed equally between the two rails. Therefore, the space between the rails at -12.0 °C is half of the total change in length.
Space between rails = ∆L / 2
Space between rails = (-1.2756 * 10^-3 m) / 2
Space between rails = -6.378 * 10^-4 m
The negative sign indicates that the rails contract at lower temperatures. Therefore, the space between the steel rails at -12.0 °C is approximately 6.378 * 10^-4 meters.