The efficiency of heat engines is 30%. Its working fluid – gas – received 10kJ from the heater.

The efficiency of heat engines is 30%. Its working fluid – gas – received 10kJ from the heater. What is the temperature of the heater if the temperature of the refrigerator is 10 degrees. How much heat was transferred to the refrigerator?

The efficiency of a heat engine is determined from the formula:
k = (Q1 – Q2) * 100% / Q1 = (1 – Q2 / Q1) * 100%,
where
Q1 = 10kJ = 10000J – the amount of heat received by the engine from the heater,
Q2 is the amount of heat transferred to the refrigerator;
From here we can find:
Q2 = Q1 * (1 – k / 100%) = 0.7 * 10000J = 7000J.
Another formula for efficiency is:
k = (T1 – T2) * 100% / T1 = (1 – T2 / T1) * 100%,
where
Т1 – heater temperature,
T2 = 10 ° C + 273 ° = 283 ° K – refrigerator temperature;
From here
T1 = T2 / (1 – k / 100%) = 283 ° K / 0.7 = 404 ° K.
t1 = T1 – 273 ° = 131 ° C.