$$2$$ moles of oxygen are mixed adiabatically with another $$2$$ moles of oxygen in mixing chamber, so that the final total pressure and temperature of the mixture become same as those of the individual constituents at, their initial states. The universal gas constant is given as $$R$$. The change in entropy due to mixing, per mole of oxygen, is given by

A rigid, insulated tank is initially evacuated. The tank is connected with a supply line through which air ( assumed to be ideal gas with constant specific heats) passes at $$1$$ $$MPa,$$ $${350^ \circ }C.$$ A valve connected with the supply line is opened and the tank is charged with air until the final pressure inside the tank reaches $$1$$ $$MPa.$$ The final temperature inside the tank.

A balloon containing an ideal gas is initially kept in an evacuated and insulated room. The balloon ruptures and the gas fills up the entire room. Which one of the following statements is TRUE at the end of above process?

$$A$$ gas expands in a frictionless piston-cylinder arrangement. The expansion process is very slow, and is resisted by an ambient pressure of $$100kPa.$$ During the expansion process, the pressure of the system (gas) remains constant at $$300$$ $$kPa.$$ The change in volume of the gas is $$0.01{m^3}.$$

The maximum amount of work that could be utilized from the above process is