To find the temperature of the low reservoir and the efficiency of the engine, we can use the Carnot efficiency formula:
Efficiency = 1 - (T_low / T_high)
where T_low is the temperature of the low reservoir and T_high is the temperature of the high reservoir.
a) The temperature of the low reservoir:
From the given information, the engine absorbs 440 J from the high temperature reservoir and loses 330 J to the low temperature reservoir. This means that the net work done by the engine per cycle is the difference between these two values:
Net work = Energy absorbed - Energy lost = 440 J - 330 J = 110 J
The formula for the net work done by the Carnot engine is:
Net work = Efficiency * Energy absorbed
Rearranging this formula and substituting the given values, we get:
Efficiency = Net work / Energy absorbed = 110 J / 440 J = 0.25
Now, we can use the Carnot efficiency formula to find the temperature of the low reservoir:
0.25 = 1 - (T_low / 227°C)
Rearranging the equation, we have:
T_low / 227°C = 1 - 0.25 = 0.75
Multiplying both sides by 227°C and solving for T_low, we get:
T_low = 0.75 * 227°C = 170.25°C
Therefore, the temperature of the low reservoir is 170.25°C.
b) The efficiency of the engine is 0.25, or 25%.