$5\mathrm{.}12$ An ideal heat engine operates in a cycle and produces

work as a result of heat transfer from a thermal

reservoir at an elevated temperature $T_h$ and by

rejecting energy to a thermal sink at $T_c.$ The effi$-$

ciency for such an ideal cycle, termed a "Carnot

cycle," is

$=1-(\frac{T_c}{T_h})$

Determine the required uncertainty in the measure$-$

ment of temperature to yield an uncertainty in

efficiency of $1\%.$ Assume errors are uncorrelated.

Use $T_h=1000K$ and $T_c=300K$