If a carnot engine receives heat from a heat source and discharge 1000J to a heat sink at temperature of 27C in each cycle, calculate the heat received and the work performed by the engine in each cycle

You need to say what the heat source temperature is. Then the efficiency can be calculated

a carnot machine operates between a hot reservoir at 200 grade C and a cold reservoir at 20 grade C.

When operated as an engine it receives 1000 KJ/kg; find the work output.
Find the COP when operates as a refrigerator and a heat pump.

To calculate the heat received by the Carnot engine, we need to know the temperatures of the heat source and the heat sink. However, you have only provided the temperature of the heat sink (27°C), but not the temperature of the heat source.

The Carnot engine operates between two heat reservoirs, called the hot reservoir and the cold reservoir. The heat source refers to the hot reservoir, and the heat sink refers to the cold reservoir.

If you provide the temperature of the hot reservoir, I can help you calculate the heat received and the work performed by the Carnot engine in each cycle. Please provide the temperature of the hot reservoir.