A salesman offers a device D which

PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · The laws of thermodynamics · The laws of thermodynamics

Thermal Physics, Ch Heat engines, refrigerators and the Carnot cycle

Problem

A salesman offers a device D which, working in a cycle, transfers

500\,\mathrm{J}

of heat per cycle from a cold reservoir at

280\,\mathrm{K}

to a hot reservoir at

560\,\mathrm{K}

, with no work supplied and no other effect: a denial of the Clausius statement. In the same laboratory stands an ordinary reversible engine R working between the same two reservoirs; per cycle R rejects

200\,\mathrm{J}

of heat to the cold reservoir. Both reservoirs are large enough that their temperatures do not change. All heats and works are magnitudes. ((a)) Find the heat R takes from the hot reservoir per cycle and the work it delivers per cycle. ((b)) D and R are run side by side, D for

n_D

cycles and R for

n_R

cycles. Find the smallest whole numbers

n_D

and

n_R

for which the cold reservoir is left exactly as it was. ((c)) For that combination, find the net heat taken from the hot reservoir and the net work delivered, and name the impossibility statement the combination denies. ((d)) Show in symbols that the construction always works: a Clausius violator moving heat

Q

from cold to hot, together with any reversible engine between the same reservoirs, can be combined into a device whose only effects are the removal of heat from a single reservoir and the delivery of an equal amount of work.

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