Solution:
An inventor claims to have devised a heat pump which exchanges heat with reservoirs at $30^\circ C$ and $260^\circ C$, and which has a thermal efficiency (or $C.O.P$) of $0.5$. Please answer the following.
\begin{parts}
\part [5] Write down the definition for the thermal efficiency (or $C.O.P$, coefficient of performance) of a heat pump.
\part [11] Is this claim believable? Please prove to get the answer.
\end{parts}
