A Carnot engine with an efficiency of 30% operates with a high-temperature reservoir at 188oC and exhausts 2000 J of heat each cycle. What are (a) the heat input per cycle and (b) the Celcius temperature of the low-temperature reservoir

a) The heat input per cycle is 2857.143 joules.

b) The temperature of the low-temperature reservoir is 49.655 °C.

Explanation:

a) The efficiency of the Carnot engine is defined by the following formula:

(1)

Where:

- Low temperature reservoir, in Kelvin.

- High temperature reservoir, in Kelvin.

 - Heat output, in joules.

- Heat input, in joules.

- Engine efficiency, no unit.

If we know that and , the heat input of the Carnot engine is:

The heat input per cycle is 2857.143 joules.

b) If we know that and , then the temperature of the low-temperature reservoir:

The temperature of the low-temperature reservoir is 49.655 °C.