Response to the following problem:
A logarithmic thermodynamic temperature scale, which can be constructed to agree with the Celsius scale at NMP-H20 and NBP-H20, is related to the Celsius scale by the formula
L = (99.974) log T - log 273.15/log 373.124 - log 273.15
Where L is any temperature on the logarithmic temperature scale and T is the corresponding Kelvin temperature on the linear temperature scale. The formula reduces to
L = 738.08 log T - 1798.26 .
(a) Calculate logarithmic temperatures for several representative temperatures between 10-3 K and 15 x 106K.
(b) Consider two different temperature ranges on the linear scale that yield the same thermal efficiency for a Carnot cycle. Calculate the temperature ranges on the logarithmic scale and draw a conclusion about efficiency on the logarithmic scale.