A Carnot engine is operating between a hot body and cold body maintained at temperatures \( T_1 \) and \( T_2 \) respectively. Consider the following three cases:
• Case-I: The temperature of the hot body is changed to \( T_1 + \Delta T \) and cold body is at \( T_2 \).
• Case-II: The temperature of the hot body is at \( T_1 \) and cold body is changed to \( T_2 + \Delta T \).
• Case-III: The temperature of the hot body is at \( T_1 \) and cold body is changed to \( T_2 - \Delta T \). The efficiency of the Carnot cycle is highest for: