Nitrogen gas (molecular weight $$28$$) is enclosed in a cylinder by a piston, at the initial condition of $$2$$ bar, $$298$$ $$K$$ and $$1\,\,{m^3}$$. In a particular process, the gas slowly expands under isothermal condition, until the volume becomes $$2{m^3}.$$ Heat exchange occurs with the atmosphere at $$298$$ $$K$$ during this process.

The work interaction for the Nitrogen gas is

Considering the relationship $$TdS=dU+PdV$$ between the entropy $$(S),$$ internal energy $$(U),$$ pressure $$(P),$$temperature $$(T)$$ and volume $$(V),$$
Which of the following statements is correct?

One kilomole of an ideal gas is throttled from an initial pressure of $$0.5$$ $$MPa$$ to $$0.1$$ $$MPa.$$ The initial temperature is $$300$$ $$K.$$ The entropy change of the universe is:

Figure below shows a reversible heat engine $${E_R}$$ having heat interactions with three constant temperature systems. Calculate the thermal efficiency of the heat engine.