A thermodynamic system is taken through the cycle abcda. The work done by the gas along the path bc is:

The correct option is Zero.

Step-by-Step Explanation:

1. Analyze the P-V diagram:
From the given pressure-volume (P-V) indicator diagram, we can identify the coordinates of the state points:
- Point a: Volume = 100 cm³, Pressure = 100 kPa
- Point b: Volume = 400 cm³, Pressure = 100 kPa
- Point c: Volume = 400 cm³, Pressure = 300 kPa
- Point d: Volume = 100 cm³, Pressure = 300 kPa

2. Analyze the path bc:
Along the path from state b to state c, the volume of the thermodynamic system remains constant at:

$V=400{\text{cm}}^3$

Since the volume does not change, the change in volume ($dV$) is zero:

$dV=0$

3. Calculate the work done:
The work done ($W$) by a gas during a thermodynamic process is given by:

$W=\int PdV$

Substituting the value of $dV=0$ into the equation:

$W=0$

Therefore, the work done by the gas along the path bc is zero.