Answer :
Final answer:
The efficiency of a Carnot engine with operating temperatures of 210°C and 45°C is 34.12%. With a work output of 910 J, the heat input for the engine is calculated to be 2667.64 J.
Explanation:
The question involves a Carnot engine, which is a theoretical engine that operates on the Carnot cycle and is known for having the maximum possible efficiency that a heat engine can achieve between two temperatures. The formula uses the temperatures of the hot (Th) and cold (Tc) reservoirs in Kelvins (K) to determine the efficiency (η) of a Carnot engine: η = 1 - (Tc / Th).
First, we convert the temperatures from Celsius to Kelvin:
For 210°C, Th = 210 + 273.15 = 483.15 K
For 45°C, Tc = 45 + 273.15 = 318.15 K
Now apply the formula to calculate efficiency:
η = 1 - (Tc / Th)
η = 1 - (318.15 / 483.15)
η = 1 - 0.6588
η = 0.3412 or 34.12%
Now, to calculate the heat input (Qin), knowing that the work output (W) is 910 J and efficiency is η = W / Qin:
910 J = 0.3412 * Qin
Qin = 910 J / 0.3412
Qin = 2667.64 J
