• # question_answer Direction: An ideal diatomic gas is confined in a cylinder A of volume ${{V}_{0}},$ this cylinder is connected to another cylinder B with the help of tube of a negligible volume. The cylinder B is fitted with a movable piston which can be adjusted from outside. Initially, the piston is adjusted so that volume of B is the same as volume of A i.e., ${{V}_{0}}$. B is evacuated and the stopcork is opened so that gas expands and occupies the volume $2{{V}_{0}}$. [System is thermally isolated from the surroundings]. Work done on the gas is [for n moles of gas] A) $nRT\text{ }\ln \text{ }2$ B) $-nRT\text{ }\ln \text{ }2$ C) $nRT$ D) $-nRT$

 [a]During compression, process is slow so it is isothermal at constant temperature T. So, work done, $W\,=\,nRT\,\ln \,\frac{{{V}_{f}}}{{{V}_{i}}}\,=-nRT\,\,\ln \,\,2$ This is the work done by the system on the surrounding, so work done by the surroundings on the system in nRT ln 2.