300 calories of heat is given to a heat engine, and it rejects 225 calories of heat. If source temperature is 227°C, then the temperature of sink will be ______ °C.

We are given: Heat supplied by the source $$Q_1 = 300$$ cal, heat rejected to the sink $$Q_2 = 225$$ cal, and source temperature $$T_1 = 227°C = 500$$ K.

First, recall that for a Carnot engine the ratio of heat rejected to heat supplied equals the ratio of sink temperature to source temperature:

$$\frac{Q_2}{Q_1} = \frac{T_2}{T_1}$$

Substituting the given values into this relation yields

$$\frac{225}{300} = \frac{T_2}{500}$$

From which we find

$$T_2 = 500 \times \frac{225}{300} = 500 \times \frac{3}{4} = 375 \text{ K}$$

Finally, converting this to Celsius gives

$$T_2 = 375 - 273 = 102°C$$

Hence, the temperature of the sink is 102 °C.