$$2$$ 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

In a steady state steady flow process taking place in a device with a single inlet and a single outlet, the work done per unit mass flow rate is given by $$W = - \int_{inlet}^{outlet} {vdp} ,$$ where $$v$$ is the specific volume and $$P$$ is the pressure. The expression for $$'W'$$ given above

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?