9 Thermo 6

# 9 Thermo 6 - Entropy the story of lost opportunities Gas...

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Entropy – the story of lost opportunities. .. vs. Gas expands without doing any mechanical work Heat transfer between a hot and cold object without mechanical work done. There was an opportunity for a spontaneous process – heat flow from T h to T c .

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Spontaneous (NOT quasi-static) expansion of a gas and heat transfer between two objects with different temperatures are both irreversible processes lost opportunities . What kind of simple reversible processes do we have in stock? isothermal adiabatic 0 = Δ U const T = Q W = Thermal reservoir with constant temperature U W Δ = 0 = Q No heat transfer at all. What do these two processes have in common?
How do we convert internal energy or heat into work? We build a heat engine. W Q U = Δ nRT PV = = PdV W Isothermal engine 0 = Δ U Q W = = 1 2 ln V V nRT W In principle one can get an unlimited amount of workE BUT it will require an infinitely large expansion! What are we going to do after the gas expands? Run it back? 100% of the heat transferred to the system is converted to workE.

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= PdV W Isothermal engine = 1 2 ln V V nRT W As the system expands all the heat transferred to the system is converted to workE. W < 0 W > 0 As the system contracts back, though, the same amount of work is done by the surroundings and all the energy is returned to the thermal reservoir.
= PdV W Adiabatic engine The positive work is now limited by the internal energy of the insulated system. But again,

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9 Thermo 6 - Entropy the story of lost opportunities Gas...

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