Consider the following two processes;
$$\left( {\rm I} \right)$$ A heat source at $$1200$$ $$K$$ loses $$2500$$ $$kJ$$ of heat to a sink at $$800$$ $$K$$
$$\left( {\rm II} \right)$$ A heat source at $$800$$ $$K$$ loses $$2000$$ $$kJ$$ of heat to a sink at $$500$$ $$K$$

Which of the following statements is true?

A cycle device operates between three thermal reservoirs, as shown in the figure. Heat is transferred to/from the cyclic device. It is assumed that heat transfer between each thermal reservoir and the cyclic device takes place across negligible temperature difference. Interactions between the cyclic device and the respective thermal reservoirs that are shown in the figure are all in the form of heat transfer.

The cyclic device can be

A vapor absorption refrigeration system is a heat pump with three thermal reservoirs as shown in the figure. A refrigeration effect of $$100$$ $$W$$ is required at $$250$$ $$K$$ when the heat source available is at $$400$$ $$K.$$ Heat rejection occurs at $$300$$ $$K.$$ The minimum value of heat required (in $$W$$) 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?