An insulated cylindrical vessel filled with an insulated piston of negligible weight and negligible thickness at the mid point of the vessel. The cylinder contains a gas at \(0^{\circ} \mathrm{C}\). When the gas is heated to \(100^{\circ} \mathrm{C}\), the piston moves through a length of \(5 \mathrm{~cm}\). Length of the cylindrical vessel in \(\mathrm{cm}\) is

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.