The efficiency of the heat engine is 30%. Its working fluid (gas) received 10 kJ of heat from the heater.

The efficiency of the heat engine is 30%. Its working fluid (gas) received 10 kJ of heat from the heater. Calculate the heater temperature if the refrigerator temperature is 20 (degrees Celsius). How much heat is transferred to the refrigerator?

Let’s write down the efficiency formulas and express the required values from them:
1) η = (T1 – T2) / T1
Tn = Tg / (1 – η) =
Tn = -0.3 * (293/1) = 418.6 (K)

2) η = (Q1 – Q2) / Q1
Q2 – given to the refrigerator
Q1 – refrigerator temperature
Q2 = Q1 * (1 – η)
Q2 = 10 * (1 – 0.3) = 7 (kJ)

Answer:
Tn = 418.6 (K)
Q2 = 7 (kJ)