A

Step 1: Identify the given values:
Heat added (Q) = 200 J
Distance moved by the piston (d) = 5 cm = 0.05 m
Spring constant (K) = 50 kN/m = 50000 N/m
Mass (m) = 60 kg.

Step 2: Calculate the force acting on the piston due to the weight:
F = m * g = 60 kg * 9.81 m/s² = 588.6 N.

Step 3: The work done against the spring when the piston moves up is given by:
Work done (W) = \frac{1}{2} Kx^2, where x = displacement of the spring. Since the piston moves 5 cm upward, the spring will also compress or stretch a small distance 'x'. Therefore, we can assume x to be equal to the piston movement.
\( W = \frac{1}{2} * 50000 N/m * (0.05 m)^2 = \frac{1}{2} * 50000 * 0.0025 = 62.5 J. \)

Step 4: Using the First Law of Thermodynamics:
\( \Delta U = Q - W \)
Where: \( \Delta U \) = change in internal energy, Q = heat added, W = work done.
Substituting the values, we get: \( \Delta U = 200 J - 62.5 J = 137.5 J. \)

Therefore, the change in internal energy of the vapor is 137.5 J.
Therefore, the answer is 137.5 J.