The gas in an ideal heat engine gives the refrigerator 65% of the heat received from the heater.

The gas in an ideal heat engine gives the refrigerator 65% of the heat received from the heater. What is the temperature of the refrigerator if the heater temperature is 520 K?

η = 65% = 0.65
Let’s write an expression to determine the efficiency of a heat engine:
η = (Tn-Tx) / Tn, where Tn is the heater temperature, Tx is the refrigerator temperature.
Let us express the temperature of the refrigerator from this expression:
Tn-Tx = Tn * η
Тх = Tн-Тн * η
Substitute the numerical values, determine the temperature of the refrigerator:
Tx = Tn-Tn * η = 520-0.67 * 520 = 171.6 K
Answer: The temperature of the refrigerator is 171.6 K.