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The figure shows a heat engine (HE) working between two reservoirs. The amount of heat $(Q_2)$ rejected by the heat engine is drawn by a heat pump (HP). The heat pump receives the entire work output $(W)$ of the heat engine. If temperatures, $T_1 >T_3>T_2$, then the relation between the efficiency $(\eta)$ of the heat engine and the coefficient of performance $\text{(COP)}$ of heat pump is

  1. $\text{COP}= \eta$
  2. $\text{COP}= 1 + \eta$
  3. $\text{COP}= \eta^{-1}$
  4. $\text{COP}= \eta^{-1} -1 $
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