What would happen in Carnot cycle if heat engine is less efficient?

[PLAGUE]

TL;DR

What would happen in Carnot cycle if heat engine is less efficient than the refrigerator?

In this cycle, if $$X$$ has efficiency greater than $$X^{'}$$, then we can show that, heat flows from cold reservoir to the hot reservoir. But this contradicts our everyday observation and we conclude that $$X$$ can not have greater efficiency than $$X^{'}$$.

But what if efficiency of $$X$$ is less than efficiency of $$X^{'}$$? Then, we can show that, $$Q_{H} > Q_{H}^{'}$$ and $$Q_{L} > Q_{L}^{'}$$, which means heat flows from hot to cold reservoir which doesn't contradict any observations. But doesn't it violate Carnot theorem that efficiency of both engine and refrigerator be same?

 

[Dale]

No, it just means X is not reversible.