A heat engine operates between a cold reservoir at temperature `T_2=300K` and a hot reservoir at temperature `T_1`. It takes 200 J of heat from the hot reservoir and delivers 120 J of heat from the hot reservoir and delivers 120 J of heat to the cold reservoir in a cycle. What could be the minimum temperature of the hot reservoir?

Explanation

To find the minimum temperature of the hot reservoir \( T_1 \) for the given heat engine, we can follow these steps:

### Step 1: Identify the given values
- Heat taken from the hot reservoir, \( Q_1 = 200 \, \text{J} \)
- Heat delivered to the cold reservoir, \( Q_2 = 120 \, \text{J} \)
- Temperature of the cold reservoir, \( T_2 = 300 \, \text{K} \)

### Step 2: Calculate the work done by the engine
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