Answer
The efficiency of a Carnot engine is given by the formula:
efficiency = (Th - Tc)/Th
where Th is the temperature of the hot reservoir and Tc is the temperature of the cold reservoir.
(a) The work done by the engine in one cycle is equal to the difference between the heat extracted from the hot reservoir and the heat rejected to the cold reservoir:
W = Qh - Qc = 2.84 kJ - 1.31 kJ = 1.53 kJ
(b) The efficiency of the engine is:
efficiency = (Th - Tc)/Th
Solving for Th, we get:
Th = Tc / (1 - efficiency)
Th = (22.5 + 273.15) K / (1 - 1.53/2.84)
Th = 588.96 K
Therefore, the efficiency of the Carnot engine is 0.457 or 45.7%, and the temperature of the hot reservoir is 588.96 K or 315.81°C.
Work Step by Step
The efficiency of a Carnot engine is given by the formula:
efficiency = (Th - Tc)/Th
where Th is the temperature of the hot reservoir and Tc is the temperature of the cold reservoir.
(a) The work done by the engine in one cycle is equal to the difference between the heat extracted from the hot reservoir and the heat rejected to the cold reservoir:
W = Qh - Qc = 2.84 kJ - 1.31 kJ = 1.53 kJ
(b) The efficiency of the engine is:
efficiency = (Th - Tc)/Th
Solving for Th, we get:
Th = Tc / (1 - efficiency)
Th = (22.5 + 273.15) K / (1 - 1.53/2.84)
Th = 588.96 K
Therefore, the efficiency of the Carnot engine is 0.457 or 45.7%, and the temperature of the hot reservoir is 588.96 K or 315.81°C.
