A cyclic device chills a cold store and exchanges no work with its surroundings: all…

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

Thermal Physics, Ch The second law, entropy and irreversibility

Problem

A cyclic device chills a cold store and exchanges no work with its surroundings: all the energy it uses arrives as heat. Per cycle it takes heat

Q_{\rm h}

from a hot reservoir at

T_{\rm h} = 800\ \mathrm{K}

, takes

Q_{\rm c} = 500\ \mathrm{J}

from the cold store at

T_{\rm c} = 250\ \mathrm{K}

, rejects heat

Q_{\rm a}

to the ambient reservoir at

T_{\rm a} = 300\ \mathrm{K}

, and returns to its initial state. All three bodies are reservoirs, each large enough that its temperature does not change. Use the book's convention in which every heat is counted as delivered to the working substance. ((a)) Use energy conservation over one cycle and the Clausius inequality

\oint \delta Q/T \le 0

to derive the smallest possible

Q_{\rm h}

per

500\ \mathrm{J}

removed from the cold store, and give its value. ((b)) A real machine of this kind uses

Q_{\rm h} = 250\ \mathrm{J}

per cycle. Evaluate the cycle sum

\oint \delta Q/T

and the total entropy created per cycle. Answer in the order: cycle sum, entropy created.

Browse the problem library