To evaluate the expression \( 14k^2 \) for \( k = 1 \), substitute \( k \) with \( 1 \):
\[ 14(1)^2 \]
Calculating \( (1)^2 \):
\[ = 14 \cdot 1 \]
Then simplify:
\[ = 14 \]
So, the value of the expression \( 14k^2 \) for \( k = 1 \) is \( \boxed{14} \).