How many times the absolute temperature of the heater is greater than the absolute temperature

How many times the absolute temperature of the heater is greater than the absolute temperature of the refrigerator, if in an ideal heat engine, work is done at 450 Joules for each kilojoule of energy received from the heater.

Given:

Q1 = 1 kJ = 1000 J;

A = 450 J;

T1 / T2 -?

Decision:

formula for the efficiency of an ideal heat engine:

Efficiency = A / Q1 * 100%,

the efficiency can also be expressed in terms of temperatures:

Efficiency = (T1 – T2) / T1 * 100% = (1 – T2 / T1) * 100%;

Efficiency = 450/1000 = 0.45;

T2 / T1 = 1 – efficiency;

T2 / T1 = 1 – 0.45 = 0.55;

T1 / T2 = 1 / 0.55 = 1.8 times.