In my studies, I've come across Kelvin's statement of the 2nd law:
It is impossible to undergo a cyclic process whose only effect is removing heat from a reservoir and generating an equivalent amount of work.
Later on, when introducing heat engines, the following is mentioned:
A heat engine produces work from heat, operating in cycles. By Kelvin's statement of the 2nd Law, that cannot be achieved with a single thermal reservoir: at least two reservoirs at different temperatures are needed.
I can see why an engine working with a single reservoir would go against Kelvin's statement. However, I can't quite see why does the 2nd law imply the necessity of a second reservoir at a temperature lower than the first. Why must that be so?