a.
The heat the engine extracts from its heat source in each cycle is 3.79 × 10⁴ J
The efficiency of the Carnot engine, ε = W/Q where W = work done per cycle = 2.5 × 10⁴ J and Q = heat extracted in each cycle.
Making Q subject of the formula, we have
Q = W/ε
Since ε = 66% = 0.66, we substitute the values of the variables into the equation for Q.
So, Q = W/ε
Q = 2.5 × 10⁴ J/0.66
Q = 3.79 × 10⁴ J
So, the heat the engine extracts from its heat source in each cycle is 3.79 × 10⁴ J
b.
The temperature of its heat source is 588.76 °C
Also, the efficiency of the Carnot engine, ε = 1 - T/T' where T = temperature of exhaust heat = 20° C = 273 + 20 = 293 K and T' = temperature of heat source.
Making T' subject of the formula, we have
T' = T/(1 - ε)
Since ε = 66 % = 0.66
Substituting the values of the variables into the equation, we have
T' = T/(1 - ε)
T' = 293 K/(1 - 0.66)
T = 293 K/0.34
T = 861.76 K
We convert this to Celsius.
T(K) = T(°C) + 273
T(°C) = T(K) - 273
T(°C) = 861.76 - 273
T(°C) = 588.76 °C
So, the temperature of its heat source is 588.76 °C
Learn more about Carnot engine here:
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