A) The amount of space must be left between adjacent rails if they are just to touch on a summer day when their temperature is 31.0 °C is; 0.6048 cm
B) The stress in the rails on a summer day when their temperature is 31.0 °C is; 86.4 × 10⁶ Pa
<h3>Linear Thermal Expansion</h3>
We are given;
Length; L = 14 m
Initial Temperature; T_i = −5 °C
Final Temperature; T_f = 31 °C
The formula for Linear Thermal Expansion is;
ΔL = L_i * α * ΔT
where;
L_i is initial length
α is thermal expansion
ΔL is change in length
ΔT is change in temperature
Now, the thermal expansion of steel from online tables is α = 1.2 × 10⁻⁵ C⁻¹
Thus;
ΔL = 14 * 1.2 × 10⁻⁵ * (31 - (-5))
ΔL = 6.048 × 10⁻³ m = 0.6048 cm
The formula to get the stress is;
σ = Y * α * ΔT
where;
Y is young's modulus of steel = 20 × 10¹⁰ Pa
α is thermal expansion
ΔT is change in temperature
Thus;
σ = 20 × 10¹⁰ × 1.2 × 10⁻⁵ × (31 - (-5))
σ = 86.4 × 10⁶ Pa
The complete question is;
Steel train rails are laid in 14.0-m long segments placed end to end. The rails are laid on a winter day when their temperature is −5 °C.
(a) How much space must be left between adjacent rails if they are just to touch on a summer day when their temperature is 31.0 °C?
(b) If the rails are originally laid in contact, what is the stress in them on a summer day when their temperature is 31.0 °C?
Read more about Linear Thermal Expansion at; brainly.com/question/6985348
