To solve this problem, we can use the formula for the efficiency of a heat engine:
Efficiency = (1 - Tlow / Thigh) * 100%
Let's assume the efficiency of the Carnot engine is x, then the efficiency of the given engine is 0.55x.
We are given that the given engine absorbs 530 J and expels 310 J. We can calculate the ratio of heat absorption to heat expulsion:
Heat Absorption / Heat Expulsion = 530 / 310
Now, we can set up the equation for the efficiency of the given engine:
0.55x = (1 - Tlow / Thigh) * 100%
To simplify the equation, let's divide both sides by 100:
0.0055x = 1 - Tlow / Thigh
Now, we can substitute the ratio of heat absorption to heat expulsion:
0.0055x = 1 - (310 / 530)
Simplifying further:
0.0055x = 1 - 0.5849
0.0055x = 0.4151
Now, let's isolate x:
x = 0.4151 / 0.0055
x = 75.56
So, the efficiency of the Carnot engine is approximately 75.56%.
Now, let's use this efficiency to find the ratio of the low temperature (Tlow) to the high temperature (Thigh) in the Carnot engine:
Efficiency = (1 - Tlow / Thigh) * 100%
75.56% = (1 - Tlow / Thigh) * 100%
Dividing both sides by 100:
0.7556 = 1 - Tlow / Thigh
Rewriting the equation:
Tlow / Thigh = 1 - 0.7556
Tlow / Thigh = 0.2444
So, the ratio of the low temperature to the high temperature in the Carnot engine is approximately 0.2444.