The gap between any two rails, each of length $l$ laid on a railway track, is equal to $x$ at $27\,^{\circ}C$. When the temperature rises to $40\,^{\circ}C$, the gap closes up. If the coefficient of linear expansion of the material of the rail is $\alpha$, the length $l$ of a rail at $27\,^{\circ}C$ is:

• A
  $\frac{x}{26\alpha}$
• B
  $\frac{x}{13\alpha}$
• C
  $\frac{2x}{13\alpha}$
• D
  $\frac{2x}{14\alpha}$