Multiple Choice
A theoretical heat engine in space could operate between the Sun's 5500°C surface and the –270.3°C temperature of intergalactic space. What would be its maximum theoretical efficiency?
23. The Second Law of Thermodynamics
The Carnot Cycle
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What is the hot reservoir temperature of a Carnot heat engine that does work each cycle while expelling to a cold reservoir?
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Verified step by step guidance1
Understand the Carnot heat engine: A Carnot engine is an idealized heat engine that operates on the reversible Carnot cycle. It has two reservoirs: a hot reservoir at temperature Th and a cold reservoir at temperature Tc. The engine absorbs heat Qh from the hot reservoir, does work W, and expels heat Qc to the cold reservoir.
Apply the first law of thermodynamics: The first law states that the energy input into the system (Qh) is equal to the work done by the system (W) plus the energy expelled (Qc). Mathematically, this is expressed as Qh = W + Qc.
Use the given values: From the problem, we know that the work done W is 120 J and the heat expelled Qc is 100 J. Substitute these values into the first law equation to find Qh: Qh = 120 J + 100 J.
Calculate the efficiency of the Carnot engine: The efficiency (η) of a Carnot engine is given by η = 1 - (Tc/Th), where Tc is the temperature of the cold reservoir and Th is the temperature of the hot reservoir. The efficiency can also be expressed as η = W/Qh.
Solve for the hot reservoir temperature Th: Use the efficiency equation η = 1 - (Tc/Th) and the calculated efficiency from step 4 to solve for Th. Substitute Tc = 300 K and the calculated Qh into the equation to find Th.
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