Transcription of Solutions to sample quiz problems and assigned problems
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Solutions to sample quiz problems and assigned problems
1 Solutions to sample quiz problems and assigned problemsSample Quiz ProblemsQuiz problem 1. Prove the expression for the Carnot efficiency for a perfectly reversible Carnot cycle using anideal :The ideal Carnot cycle consists of four segments as follows (1) An isothermal expansion during whichheatQHis added to the system at temperatureTH; (2) an adiabatic expansion during which the gas cools fromtemperatureTHtoTC; (3) An isothermal compression during which heatQCis extracted from the system to a coldreservoir at temperatureTC; (4) Adiabatic compression during which the temperature of the gas rises efficiency of the engine is given by =W/QH, whereWis the useful work done by the system andQHis theheat added to the system. This is a thermodynamic cycle provided it is carried out reversibly ( kept very closeto equilibrium), and then the internal energy is the same at the beginning and the end of the cycle. In that case,dU= 0, andWtotal=QH QL, so we can also write the efficiency as = 1 QLQH= 1 TL STH S= 1 TLTH(1)The introduction of Entropy by Clausius greatly simplified understanding of engines.
1 Solutions to sample quiz problems and assigned problems Sample Quiz Problems Quiz Problem 1. Prove the expression for the Carnot e ciency for a perfectly reversible Carnot cycle using an
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